ALBERT

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): Jean-Lou Pfister, Olivier Marquet, Marco Carini〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The stability analysis of elastic structures strongly coupled to incompressible viscous flows is investigated in this paper, based on a linearization of the governing equations formulated with the Arbitrary-Lagrangian–Eulerian method. The exact linearized formulation, previously derived to solve the unsteady non-linear equations with implicit temporal schemes, is used here to determine the physical linear stability of steady states. Once discretized with a standard finite-element method based on Lagrange elements, the leading eigenvalues/eigenmodes of the linearized operator are computed for three configurations representative for classical fluid–structure interaction instabilities: the vortex-induced vibrations of an elastic plate clamped to the rear of a rigid cylinder, the flutter instability of a flag immersed in a channel flow and the vortex shedding behind a three-dimensional plate bent by the steady flow. The results are in good agreement with instability thresholds reported in the literature and obtained with time-marching simulations, at a much lower computational cost. To further decrease this computational cost, the equations governing the solid perturbations are projected onto a reduced basis of free-vibration modes. This projection allows to eliminate the extension perturbation, a non-physical variable introduced in the ALE formalism to propagate the infinitesimal displacement of the fluid–solid interface into the fluid domain.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): Zhao Wang, Amit Subhash Shedbale, Sachin Kumar, Leong Hien Poh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A localizing gradient damage model with micro inertia effect is proposed for the dynamic fracture of quasi-brittle materials. The objective is to achieve mesh independent solutions, and to avoid spurious effects associated with the conventional nonlocal enhancement. The proposed localizing gradient damage model closely resembles the conventional gradient enhancement, albeit with an interaction domain that decreases with damage, complemented by a micro inertia effect. We first consider a classical crack branching problem, where the localizing gradient damage model is shown to resolve the mesh sensitivity issue, as well as to correctly reproduce the crack profile. Moreover, the micro inertia effect is observed to retard the crack velocity. Next, the tensile loading of a Polymethyl Methacrylate plate is considered. It is shown that the proposed model effectively captures the experimentally observed transition of crack profiles as the loading rate increases, i.e. from a straight crack propagation, to sub-branching, and finally to macro branching. Numerical results in terms of crack patterns, crack velocities, and fracture energies are in good agreement with the experimental data. To furthermore demonstrate the superior performance of the localizing gradient damage model, the macro branching problem is solved using the conventional gradient enhancement with micro inertia. It is shown that a spurious damage growth and an erroneous interaction between closely spaced cracks suppress the development of macro branching, even though reasonable values are obtained for the fracture energy and crack velocity. The localizing gradient damage model is able to fully resolve these issues.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): D. Xiao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A novel error estimation method for the parametric non-intrusive reduced order model (P-NIROM) based on machine learning is presented. This method relies on constructing a set of response functions for the errors between the high fidelity full model solutions and P-NIROM using machine learning method, particularly, Gaussian process regression method. This yields closer solutions agreement with the high fidelity full model. The novelty of this work is that it is the first time to use machine learning method to derive error estimate for the P-NIROM. The capability of the new error estimation method is demonstrated using three numerical simulation examples: flow past a cylinder, dam break and 3D fluvial channel. It is shown that the results are closer to those of the high fidelity full model when considering error terms. In addition, the interface between two phases of dam break case is captured well if the error estimator is involved in the P-NIROM.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): M. Goudarzi, A. Simone〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We report the results of a comparative analysis of mesh independent discrete inclusion models and point out some shortcomings of classical approaches in the approximation of the strain field across an inclusion (artificial continuity) and the slip profile along an inclusion (oscillatory behavior). We also present novel embedded reinforcement models based on partition of unity enrichment strategies, adaptive 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si246.svg"〉〈mi〉h〈/mi〉〈/math〉-refinement, and order/regularity extensions. These novel models are assessed by means of mesh convergence studies and it is shown that they improve the quality of the solution by significantly decreasing local spurious oscillations in the slip profile along an inclusion.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): C. Hermange, G. Oger, Y. Le Chenadec, D. Le Touzé〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A 3D fluid–structure coupling between Smoothed Particle Hydrodynamics (SPH) and Finite Element (FE) methods is proposed in this paper, with its application to complex tire hydroplaning simulations on rough ground. The purpose of this work is to analyze the SPH–FE coupling capabilities for modeling efficiently such a complex phenomenon. On the fluid side, the SPH method is able to handle the three complex interfaces of the hydroplaning phenomenon: free-surface, ground/fluid and fluid/tire interfaces. On the solid side, the FE method is used for its ability to treat tire–ground contact. A new algorithm dedicated to such SPH–FE coupling strategies is proposed to optimize the computational efficiency through the use of differed time steps between fluid and solid solvers. This way, the number of calls to the FE solver is minimized while maintaining the accuracy and stability of the coupling. The ratio between these respective time steps relies on a control procedure based on pressure loading. The present 3D SPH–FE model is first validated with different academic test cases and experimental data before considering the complex problem of the 3D hydroplaning simulations. Hydroplaning simulations are performed and analyzed on 3D configurations involving both smooth and rough grounds.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 September 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 354〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): Liyang Xu, Zhenzhou Lu, Luyi Li, Yan Shi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Traditional sensitivity analysis methods for the model with correlated inputs and univariate output fail to provide satisfactory results for multivariate output. In this work, we first establish a reasonable contribution classification for the univariate output with the correlated input. Then the covariance decomposition method is extended to the case of correlated inputs as a reference, and the vector projection sensitivity index is extended to aggregate the correlated and uncorrelated contributions of the input to multiple outputs. The definition of the new sensitivity index is based on the vector projection, which can take into account both uncertainties and correlations among multiple outputs by projecting the conditional variance vector (built by the full marginal variance contributions) on the unconditional variance vector (built by unconditional variance magnitudes and correlation of the multiple outputs). The mathematical properties of the extended vector projection sensitivity index are discussed and its relations with other existing sensitivity indices are highlighted. Two numerical examples and two engineering examples about an aircraft structure are employed to illustrate the validity and potential benefits of the extended vector projection sensitivity index.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): Yunfei Ma, Jiahuan Cui, Nagabhushana Rao Vadlamani, Paul Tucker〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The Immersed Boundary Method has been used to simulate a range of fundamental flows and turbulence. Such studies have demonstrated the method’s promising applicability for engineering analysis. However, to the authors’ knowledge, flows in coupled components or in scenarios with coupled physics, such as rotor–stator interaction, fan–intake interaction, aeroelastics, aeroacoustics, etc., are still rarely investigated using high-fidelity methods. Due to its high computational costs, the complexity of geometry meshing process and the requirement for moving boundaries limit the investigation of flows in such environments. Previous research suggests that high-fidelity simulations with an acceptable geometry modelling strategy may tackle these issues and provide useful insights. There exists a hierarchy of geometry modelling methods which includes the conventional Directly Mesh Resolving (DMR) method, the Immersed Boundary Method (IBM), and the IBM with Smeared Geometry (IBMsg, or eIBMg). The present research proposes an alternative to these approaches in the form of the Euler IBM with local force (eIBMl) by imposing a distribution function generated from blade configuration. Compared to the eIBMg, this method can include more realistic flow physics within each blade passage without smearing its geometry. This method is applied to the study of fan–intake interaction focusing on the transport of inlet distortion through blade passages and pressure wave propagation.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Delfim Soares〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, a simple, stable, non-iterative, uncoupled formulation is proposed for nonlinear pore-dynamic analyses. Here, each phase of the coupled problem is treated separately, uncoupling the governing equations of the porous model. Thus, simpler, smaller and better conditioned systems of equations are obtained, providing a more efficient numerical approach. In addition, in the proposed technique, solution is carried out without considering any iterative computation, even when nonlinear models are regarded, further improving the effectiveness of the method. Incompressible and impermeable media may also be directly analysed by the new formulation, without requiring any special discretization procedure, as it is the case in standard analyses. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the new technique.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Byungseong Ahn, Hyuk Lee, Joong Seok Lee, Yoon Young Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A numerical method based on topology optimization is developed for designing a metasurface that anomalously reflects longitudinal elastic waves. While the analysis and design of metasurfaces and metamaterials have received much attention recently, no numerical method to design elastic metasurfaces for anomalous reflection has been explored. Here, we formulate a density-based topology optimization suitable for finding a set of phase-delaying unit cells forming a metasurface that anomalously reflects longitudinal waves impinged upon it. Each unit cell is designed to yield the specific phase delay between the incident and reflected elastic waves. The transfer matrix approach using the averaged finite element results is employed to efficiently and accurately calculate the phase delay while the wave phenomena are analyzed by the finite element analysis. As case studies, metasurfaces converting normally incident longitudinal waves to anomalously reflected longitudinal waves were designed. Various target anomalous reflection angles were considered including the extreme reflection angle of 90°. To investigate the numerical aspect of the developed method, we investigated the effect of the sizes of the unit cells, both along the perpendicular and normal directions to the wave incidence. The mesh dependence issue was also investigated. Finally, we applied the developed topology optimization method to design metasurfaces for wave focusing and trapping in a waveguide.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Delfim Soares〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a stabilized, locally defined, explicit approach is considered to analyse coupled acoustic–elastic wave propagation models. In this sense, a modified central difference method is applied, which performs adapting itself along the solution process, considering the properties and results of the model, as well as the relations between the adopted temporal and spatial discretizations. The proposed technique enables stabilized decoupled analyses, allowing each subdomain of the coupled model to be handled separately, without considering stability restrictions for the temporal discretization, providing a very versatile and efficient methodology. In addition, the new approach is designed as a single-solve framework based on reduced systems of equations, which further greatly improves the efficiency of the technique. The new method enables adaptive algorithmic dissipation in the higher modes and it is highly accurate, simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented at the end of the manuscript, illustrating the performance and effectiveness of the new approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Bin Xie, Xi Deng, Shijun Liao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this article, we developed an unstructured fluid solver based on finite volume framework for the low-Mach number compressible flows. The present method, so-called FVMS3 (Finite Volume method based on Merged Stencil with 3rd-order reconstruction) formulates two different numerical procedures for spatial reconstructions based on the quadratic polynomial which is performed by using least-square approximations on a merged stencil. In order to improve the reconstruction for discontinuities, we propose the limiting projection approach and smoothness adaptive fitting (SAF) scheme to suppress the numerical oscillation and limit the numerical dissipation. The resulting discretization algorithm that combines FVMS3 with SAF-based limiting projection scheme has third-order accuracy and resolves both smooth and non-smooth solutions with excellent quality. Additionally, a novel numerical model has been proposed by introducing the advection upstream splitting method (AUSM) flux into the pressure projection formulation which results in a unified scheme that works uniformly up to the incompressible limit. The fluid solver that integrates all above new efforts provides high-fidelity solutions for compressible viscous flows particularly for the low Mach regime. The performance of this new solver is verified by numerous benchmark tests. Our numerical results show that the proposed scheme gives accurate and robust solutions for a wide spectrum of test problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Felix Scholz, Bert Jüttler〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a novel technique for the numerical integration of trivariate functions on trimmed domains. In our setting, we assume that the trimming surface is defined implicitly. Our approach combines a linear approximation of the trimming surface with a correction term. The latter term makes it possible to achieve a cubic convergence rate, which is one order higher than the rate obtained by using the linear approximation only. We also present numerical experiments that demonstrate the method’s potential for applications in isogeometric analysis.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Ping-Ping Wang, Zi-Fei Meng, A-Man Zhang, Fu-Ren Ming, Peng-Nan Sun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents an improved particle shifting technology (IPST) for smoothed particle hydrodynamics (SPH). It allows particles in the vicinity of the free-surface to be shifted in all the directions in case they are not uniformly distributed, rather than just shifted tangentially to the free-surface in some conventional particle shifting technologies. Therefore, with the new technique, the imprecise shifting due to the inaccurate evaluations of the local normal and tangential vectors of the free-surface can be avoided, and a more uniform particle distribution near the free-surface can be obtained even for long-term simulations, which improves the accuracy and stability of the SPH method. Besides, by combining the advantages of two existing free-surface detection methods, an optimized detection approach is provided. It is capable of detecting the free-surface particles accurately, and meanwhile, it is easier to implement and requires lower computational costs, especially for three-dimensional problems. Several numerical tests show that the proposed IPST and the optimized free-surface detection method are robust and accurate for the simulation of a variety of free-surface flows.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): T. Hirschler, R. Bouclier, D. Dureisseix, A. Duval, T. Elguedj, J. Morlier〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Originally, Isogeometric Analysis is aimed at using geometric models for the structural analysis. The actual realization of this objective to complex real-world structures requires a special treatment of the non-conformities between the patches generated during the geometric modeling. Different advanced numerical tools now enable to analyze elaborated multipatch models, especially regarding the imposition of the interface coupling conditions. However, in order to push forward the isogeometric concept, a closer look at the algorithm of resolution for multipatch geometries seems crucial. Hence, we present a dual Domain Decomposition algorithm for accurately analyzing non-conforming multipatch Kirchhoff–Love shells. The starting point is the use of a Mortar method for imposing the coupling conditions between the shells. The additional degrees of freedom coming from the Lagrange multiplier field enable to formulate an interface problem, known as the one-level FETI problem. The interface problem is solved using an iterative solver where, at each iteration, only local quantities defined at the patch level (i.e. per sub-domain) are involved which makes the overall algorithm naturally parallelizable. We study the preconditioning step in order to get an algorithm which is numerically scalable. Several examples ranging from simple benchmark cases to semi-industrial problems highlight the great potential of the method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Michael C.H. Wu, Heather M. Muchowski, Emily L. Johnson, Manoj R. Rajanna, Ming-Chen Hsu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The transcatheter aortic valve replacement (TAVR) has emerged as a minimally invasive alternative to surgical treatments of valvular heart disease. TAVR offers many advantages, however, the safe anchoring of the transcatheter heart valve (THV) in the patient’s anatomy is key to a successful procedure. In this paper, we develop and apply a novel immersogeometric fluid–structure interaction (FSI) framework for the modeling and simulation of the TAVR procedure to study the anchoring ability of the THV. To account for physiological realism, methods are proposed to model and couple the main components of the system, including the arterial wall, blood flow, valve leaflets, skirt, and frame. The THV is first crimped and deployed into an idealized ascending aorta. During the FSI simulation, the radial outward force and friction force between the aortic wall and the THV frame are examined over the entire cardiac cycle. The ratio between these two forces is computed and compared with the experimentally estimated coefficient of friction to study the likelihood of valve migration.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): SeonHong Na, Eric C. Bryant, WaiChing Sun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Nick Pepper, Francesco Montomoli, Sanjiv Sharma〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉This work presents a framework for upscaling uncertainty in multiscale models. The problem is relevant to aerospace applications where it is necessary to estimate the reliability of a complete part such as an aeroplane wing from experimental data on coupons. A particular aspect relevant to aerospace is the scarcity of data available.〈/p〉 〈p〉The framework needs two main aspects: an upscaling equivalence in a probabilistic sense and an efficient (sparse) Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. The upscaling equivalence is defined by a Probability Density Function (PDF) matching approach. By representing the inputs of a coarse-scale model with a generalised Polynomial Chaos Expansion (gPCE) the stochastic upscaling problem can be recast as an optimisation problem. In order to define a data driven framework able to deal with scarce data a Sparse Approximation for Moment Based Arbitrary Polynomial Chaos is used. Sparsity allows the solution of this optimisation problem to be made less computationally intensive than upscaling methods relying on Monte Carlo sampling. Moreover this makes the PDF matching method more viable for industrial applications where individual simulation runs may be computationally expensive. Arbitrary Polynomial Chaos is used to allow the framework to use directly experimental data. Finally, the difference between the distributions is quantified using the Kolmogorov–Smirnov (KS) distance and the method of moments in the case of a multi-objective optimisation. It is shown that filtering of dynamical information contained in the fine-scale by the coarse model may be avoided through the construction of a low-fidelity, high-order model.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Ruochun Zhang, Xiaoping Qian〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents triangulation-based Isogeometric Analysis of the Cahn–Hilliard phase-field model. The Cahn–Hilliard phase-field model is governed by a time-dependent fourth-order partial differential equation. The corresponding primal variational form involves second-order operators, making it difficult to be directly analyzed with traditional 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si220.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msup〉〈/math〉 finite element analysis. In this paper, we construct 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si67.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉 Bernstein–Bézier simplicial elements through macro-element techniques, including various triangle-split based macro-elements in both 2D and 3D space. We extend triangulation-based isogeometric analysis to solving the primal variational form of the Cahn–Hilliard equation. We validate our method by convergence analysis, showing the nodal and degree-of-freedom advantages over 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si220.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msup〉〈/math〉 Finite Element Analysis. We then demonstrate detailed system evolution from randomly perturbed initial conditions in periodic two-dimensional squares and three-dimensional cubes. We incorporate an adaptive time-stepping scheme in these numerical experiments. Our numerical study demonstrates that triangulation-based isogeometric analysis offers optimal convergence and time step stability, is applicable to complex geometry and allows local refinement.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Jiaying Gao, Modesar Shakoor, Hiroshi Jinnai, Hiroshi Kadowaki, Eisuke Seta, Wing Kam Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a computational procedure combining experimental data and interphase inverse modeling is presented to predict filled rubber compound properties. The Fast Fourier Transformation (FFT) based numerical homogenization scheme is applied on the high quality filled rubber 3D Transmission Electron Microscope (TEM) image to compute its complex shear moduli. The 3D TEM filled rubber image is then compressed into a material microstructure database using a novel Reduced Order Modeling (ROM) technique, namely Self-consistent Clustering Analysis (a two-stage offline database creation from training and learning, followed by data compression via unsupervised learning, and online prediction approach), for improved efficiency and accuracy. An inverse modeling approach is formulated for quantitatively computing interphase complex shear moduli in order to understand the interphase behaviors. The two-stage SCA and the inverse modeling approach formulate a three-step prediction scheme for studying filled rubber, whose loss tangent curve can be computed in agreement with test data.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Zeng Meng, Zhuohui Zhang, Dequan Zhang, Dixiong Yang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉To achieve an optimal design of complicated structures with stochastic parameters, the reliability-based design optimization (RBDO) usually needs to handle the nested double optimization loops, which results in unbearable computational cost. In this paper, a new active learning method for RBDO combining with Kriging metamodel and accelerated chaotic single loop approach (AK-ACSLA) is developed, in which the most probable learning function (MPLF) is proposed to search the most probable point instead of the limit state function in entire design space with an active learning behavior. To ensure the high efficiency, the system’s most probable learning function (SMPLF) is further constructed to solve the RBDO problem of series system with multiple probabilistic constraints, and then the ACSLA is proposed by taking full advantage of chaos feedback control methodology for guaranteeing the validity of AK-ACSLA. Nonlinear mathematical examples and complex RBDO engineering examples illustrate the high efficiency and accuracy of AK-ACSLA through comparison with both existing gradient-based methods and active learning methods.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Dmytro Pivovarov, Reza Zabihyan, Julia Mergheim, Kai Willner, Paul Steinmann〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Due to high computational costs associated with stochastic computational homogenization, a highly complex random material microstructure is often replaced by simplified, parametric, ergodic, and sometimes periodic models. This replacement is often criticized in the literature due to unclear error resulting from the periodicity and ergodicity assumptions. In the current contribution we perform a validation of both assumptions through various numerical examples. To this end we compare large-scale non-simplified and non-ergodic models with simplified, ergodic, and periodic solutions. In addition we analyze the Hill–Mandel condition for stochastic homogenization problems and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions. As an example, we propose two novel stochastic periodic boundary conditions which possess a clear physical meaning. The effect of these novel periodic boundary conditions is also analyzed by comparing with non-ergodic simulation results.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Emmanouil G. Kakouris, Savvas P. Triantafyllou〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly defined crack density functional. The particular case of impact driven fracture is treated by employing a discrete field approach within the material point method setting. In this, the equations of motion and phase field governing equations are solved independently for each discrete field using a predictor–corrector algorithm. Contact at the interface is resolved through frictional contact conditions. The proposed method is verified using analytical predictions. The influence of surface energy anisotropy and loading conditions on the resulting crack paths is assessed through a set of benchmark problems. Comparisons are made with the standard Phase Field Finite Element Method and experimental observations.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): C. Jiang, J.W. Li, B.Y. Ni, T. Fang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Recently the authors proposed the interval process model for dynamic uncertainty quantification and based on this further developed a kind of non-probabilistic analysis method called ‘non-random vibration analysis method’ to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to become an effective supplement to the traditional random vibration theory. In this paper, some significant improvements are made for the interval process model and the non-random vibration analysis method, making them not only more rigorous in theory but also more practical in engineering. Firstly, the definitions and relevant conceptions of interval process model are further standardized and improved, and in addition some new conceptions such as the interval process vector and the cross-covariance function matrix are complemented. Secondly, this paper proposes the important conceptions of limit and continuity of interval process, based on which the differential and integral of interval process are defined. Thirdly, the analytic formulation of dynamic response bounds is deduced for both of the linear single degree of freedom (SDOF) vibration system and the multiple degree of freedom (MDOF) vibration system, providing an important theoretical basis for non-random vibration analysis. Fourthly, this paper also gives the formulation and corresponding numerical methods of structural dynamic response bounds based on finite element method (FEM) for complex continuum problems, effectively enhancing the applicability of non-random vibration analysis in engineering. Finally, four numerical examples are investigated to demonstrate the effectiveness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo, Xianfeng Gu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉This work proposes a novel metric based algorithm for quadrilateral mesh generating. Each quad-mesh induces a Riemannian metric satisfying special conditions: the metric is a flat metric with cone singularities conformal to the original metric, the total curvature satisfies the Gauss–Bonnet condition, the holonomy group is a subgroup of the rotation group 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mo〉{〈/mo〉〈msup〉〈mrow〉〈mi〉e〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mi〉k〈/mi〉〈mi〉π〈/mi〉〈mo〉∕〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉}〈/mo〉〈/mrow〉〈/math〉, there is cross field obtained by parallel translation which is aligned with the boundaries, and its streamlines are finite geodesics. Inversely, such kind of metric induces a quad-mesh. Based on discrete Ricci flow and conformal structure deformation, one can obtain a metric satisfying all the conditions and obtain the desired quad-mesh.〈/p〉 〈p〉This method is rigorous, simple and automatic. Our experimental results demonstrate the efficiency and efficacy of the algorithm.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Shan Tang, Gang Zhang, Hang Yang, Ying Li, Wing Kam Liu, Xu Guo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Solving three-dimensional boundary-value engineering problems numerically requires material laws. However, it is difficult to build the material laws in three dimension, since the material behaviors are usually measured by one-dimensional uniaxial tension/compression experiments. In this way, the material behavior in the three-dimension is ‘compressed’ into one-dimensional data. Here we propose a new method, coined MAP123 (map data from one-dimension to three-dimension), to decompress the one-dimensional data into three dimension for nonlinear elastic material modeling without the construction of analytic mathematical function for the material law. The decomposition of stress and strain into deviatoric and spherical parts for isotropic nonlinear elastic materials at finite deformation makes this data-driven approach work quite well. Several examples are used to demonstrate the capability of MAP123, such as a rectangular plate with a circular hole under uniaxial tension. Corresponding experiments are also carried out to further verify the MAP123 method. Based on the proposed approach, uniaxial experiment is suggested to measure the deformation in three directions not only the force and extension along the loading direction. Limitation of the proposed MAP123 approach is also discussed.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): D. Thomas Seidl, Assad A. Oberai, Paul E. Barbone〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A persistent challenge present in inverse or parameter estimation problems with interior data is how to deal with uncertainty in the boundary conditions employed in the forward or state model. In this work we focus on a linear plane stress inverse elasticity problem with measured displacement data where one component of the measured displacement field is known with considerably greater precision than the other. This situation is commonly encountered when the displacement field is measured using ultrasound or optical coherence tomography. We present a novel computational formulation in which no displacement or traction boundary conditions are assumed. The formulation results in coupling the state and adjoint equations, that are typically uncoupled when a well-posed state model is available. Two variants of residual-based stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Arash Mohammadi, Mehrdad Raisee〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the current paper efficient uncertainty quantification (UQ) of high dimensional stochastic fields is performed via a bi-fidelity surrogate model. The method is based on combination of proper orthogonal decomposition (POD) and Kriging method. In the developed method, the trend function of the Kriging model is estimated via a low cost POD, whilst the stochastic Gaussian contribution is tuned using a limited number of high-fidelity computations. The proposed method is applied to three test cases, including a highly nonlinear test function, thermally driven flow in a cavity with stochastic wall temperatures and turbulent heat transfer in a ribbed channel with stochastic heat flux boundary condition. Implementing both POD and POD–Kriging methods leads to significant reduction of computational cost in comparison to the classical full polynomial chaos expansion (PCE) with least cost saving of more than 60%. Furthermore, in all cases combined POD–Kriging method performs either superior or at least similar to the POD method. More specifically, in surrogate models with lower number of low- and high-fidelity samples greater gains in accuracy are obtained. Consequently, for a specific level of accuracy, POD–Kriging method requires lower computational cost.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): M.F. Wakeni, B.D. Reddy〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The generalized thermal model is a thermodynamically consistent extension of the classical Fourier’s law for describing thermal energy transportation which is very relevant to applications involving very small length, time scales and/or at extremely low temperatures. Under such conditions, thermal propagation has been observed to manifest as waves, a phenomenon widely referred to as second sound effect. However, this is in contrast to the paradoxical prediction of the Fourier’s model that thermal disturbances propagate with infinite speed. In this work, we review the nonlinear model based on the theory of Green and Naghdi for thermal conduction in rigid bodies and present its implementation within a class of space–time methods. The unconditional stability of the time-discontinuous Galerkin method without restriction over the grid structure of the space–time domain is proved. We also perform a number of numerical experiments to study the convergence properties and analyze the thermal response of materials under short-pulsed laser heating in two space dimensions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Kyoungsoo Park, Heng Chi, Glaucio H. Paulino〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field can be further explored and developed. Thus, in this paper, we employ the virtual element method for non-convex discretizations of elastodynamic problems in 2D and 3D using an explicit time integration scheme. In the formulation, a diagonal matrix-based stabilization scheme is proposed to improve performance and accuracy. To address efficiency, a critical time step is approximated and verified using the maximum eigenvalue of the local (rather than global) system. The computational results demonstrate that the virtual element method is able to consistently handle general nonconvex elements and even non-simply connected elements, which can lead to convenient modeling of arbitrarily-shaped inclusions in composites.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Arman Shojaei, Farshid Mossaiby, Mirco Zaccariotto, Ugo Galvanetto〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper introduces an effective way to equip the standard finite element method (FEM) for the solution of transient scalar wave propagation problems in unbounded domains. Similar to many other methods, we truncate the unbounded domain at an artificial boundary and convert the problem into a bounded one by prescribing appropriate absorbing boundary conditions (ABCs) at the truncating boundary. In the present method, the ABCs are time-dependent, and they are constructed by a simple collocation approach which is local in space and time. Therefore, the method does not make use of any routine schemes such as Fourier and Laplace transform. We shall show that the method is simple, and it can be easily applied to an explicit time domain FEM approach so that the sparsity of the FEM scheme (as well as its efficiency) can be preserved. The proposed method does not require any auxiliary variables as well as any approximating differential operators. This feature roots from the fact that here the ABCs are Dirichlet-type (or first-type) and thus they can be easily imposed to the corresponding boundaries. Therefore, the method shares some similarities with the conventional 1st and 2nd order ABC methods in terms of the simplicity of implementation. The method employs basis functions that exactly satisfy the governing and dispersion wave equations. The basis function can be easily adjusted to act as outgoing waves transmitting energy from the interior domain (near field) towards exterior domain (far field); i.e, they can cope with satisfaction of radiation boundary conditions. Several numerical examples are presented to evaluate the performance and to demonstrate the effectiveness of the approach. We shall show that the present method is capable of yielding results with a proper level of accuracy, similar to that of the perfectly matched layers method (PMLs), and it performs stably even in the case of long-term computations.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 355〈/p〉 〈p〉Author(s): Jize Zhang, Alexandros A. Taflanidis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Markov Chain Monte Carlo (MCMC) simulation has a considerable computational burden when the target probability density function (PDF) evaluation involves a black-box, potentially computationally-expensive, numerical model. A novel framework to accelerate MCMC is developed here for such applications. It leverages a Kriging surrogate model approximation to the target PDF to improve computational efficiency, while preserves convergence properties to the exact target PDF, avoiding potential accuracy problems introduced through the surrogate model error. The approach relies on the delayed-rejection (DR) scheme and combines the rapid exploration characteristics of global (independent) proposals with the local search robustness of random walk proposals under the MCMC setting. The global proposal is chosen as the Kriging-based target PDF approximation. This proposal may resemble, depending on the surrogate model error, the actual target PDF very well, and therefore can provide significant computational benefits, including fast convergence of the Markov chain to its stationary distribution and, more importantly, low correlation between samples. At each MCMC step a candidate sample is generated from the independent proposal. If rejected, DR allows an extra random walk around the current sample. The DR step guarantees convergence to the actual target PDF, circumventing robustness problems that may arise when the Kriging-based independent proposal offers a poor approximation to (i.e., underestimates) the actual target PDF. The overall computational efficiency is further improved through an adaptive updating of the Kriging surrogate model during the MCMC sampling phase by extracting information from candidate samples whose inclusion in the training database can substantially enhance Kriging’s accuracy. The computational efficiency and robustness of the established algorithm, termed Adaptive Kriging Delayed Rejection Adaptive Metropolis algorithm(AK-DRAM), are demonstrated in two analytical benchmark problems and two engineering problems focusing on conditional failure sample simulation and Bayesian inference.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Enzo Marino, Josef Kiendl, Laura De Lorenzis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We propose a novel approach to the implicit dynamics of shear-deformable geometrically exact beams, based on the isogeometric collocation method combined with the Newmark time integration scheme extended to the rotation group SO(3). The proposed formulation is fully consistent with the underlying geometric structure of the configuration manifold. The method is highly efficient, stable, and does not suffer from any singularity problem due to the (material) incremental rotation vector employed to describe the evolution of finite rotations. Consistent linearization of the governing equations, variables initialization and update procedures are the most critical issues which are discussed in detail in the paper. Numerical applications involving very large motions and different boundary conditions demonstrate the capabilities of the method and reveal the critical role that the high-order approximation in space may have in improving the accuracy of the solution.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Dawei Song, Nicholas Hugenberg, Assad A. Oberai〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Jinhyun Choo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Local (element-wise) mass conservation is often highly desired for numerical solutions to coupled poromechanical problems. As an efficient numerical method featuring this property, mixed continuous Galerkin (CG)/enriched Galerkin (EG) finite elements have recently been proposed in which piecewise constant functions are enriched to the pore pressure interpolation functions of the conventional mixed CG/CG elements. While this enrichment of the pressure space provides local mass conservation, it unavoidably alters the stability condition for mixed finite elements. Because no stabilization method has been available for the new stability condition, high-order displacement interpolation has been required for mixed CG/EG elements if undrained condition is expected. To circumvent this requirement, here we develop stabilized formulations for the mixed CG/EG elements that permit equal-order interpolation functions even in the undrained limit. We begin by identifying the inf–sup condition for mixed CG/EG elements by phrasing an enriched poromechanical problem as a twofold saddle point problem. We then derive two types of stabilized formulations, one based on the polynomial pressure projection (PPP) method and the other based on the fluid pressure Laplacian (FPL) method. A key finding of this work is that both methods lead to stabilization terms that should be augmented only to the CG part of the pore pressure field, not to the enrichment part. The two stabilized formulations are verified and investigated through numerical examples that involve various conditions spanning 1D to 3D, isotropy to anisotropy, and homogeneous to heterogeneous domains. The methodology presented in this work may also help stabilize other types of mixed finite elements in which the constraint field is enriched by additional functions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): Daniel Garcia, David Pardo, Victor M. Calo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the continuity is reduced, the number of degrees of freedom in the system grows. The resulting discretization spaces are finer than standard maximal continuity IGA spaces. Despite the increase in the number of degrees of freedom, these finer spaces deliver simulation results faster with direct solvers than both traditional finite element and isogeometric analysis for meshes with a fixed number of elements. In this work, we analyze the impact of continuity reduction on the number of Floating Point Operations (FLOPs) and computational times required to solve fluid flow and electromagnetic problems with structured meshes and uniform polynomial orders. Theoretical estimates show that for sufficiently large grids, an optimal continuity reduction decreases the computational cost by a factor of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mi mathvariant="script"〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/math〉. Numerical results confirm these theoretical estimates. In a 2D mesh with one million elements and polynomial order equal to five, the discretization including an optimal continuity pattern allows to solve the vector electric field, the scalar magnetic field, and the fluid flow problems an order of magnitude faster than when using a highly continuous IGA discretization. 3D numerical results exhibit more moderate savings due to the limited mesh sizes considered in this work.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): E. Benvenuti, A. Chiozzi, G. Manzini, N. Sukumar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we propose the extended virtual element method (X-VEM) to treat singularities and crack discontinuities that arise in the Laplace problem. The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes, wherein the basis functions are implicit (virtual)—they are not known explicitly nor do they need to be computed within the problem domain. Suitable projection operators are used to decompose the bilinear form on each element into two parts: a consistent term that reproduces the first-order polynomial space and a correction term that ensures stability. A similar approach is pursued in the X-VEM with a few notable extensions. To capture singularities and discontinuities in the discrete space, we augment the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis (partition-of-unity) functions with enrichment functions. For discontinuities, basis functions are discontinuous across the crack and for singularities a weakly singular enrichment function that satisfies the Laplace equation is chosen. For the Laplace problem with a singularity, we devise an extended projector that maps functions that lie in the extended virtual element space onto linear polynomials and the enrichment function, whereas for the discontinuous problem, the consistent element stiffness matrix has a block-structure that is readily computed. An adaptive homogeneous numerical integration method is used to accurately and efficiently (no element-partitioning is required) compute integrals with integrands that are weakly singular. Once the element projection matrix is computed, the same steps as in the standard VEM are followed to compute the element stabilization matrix. Numerical experiments are performed on quadrilateral and polygonal (convex and nonconvex elements) meshes for the problem of an 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si684.svg"〉〈mi〉L〈/mi〉〈/math〉-shaped domain with a corner singularity and the problem of a cracked membrane under mode III loading, and results are presented that affirm the sound accuracy and demonstrate the optimal rates of convergence in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si706.svg"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉 norm and energy of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Chong Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In many mechanical engineering practices, the sample information is usually imprecise due to the complex objective environment or various subjective cognitions. In this study, a kind of inverse problem for identifying the uncertain system parameters with imprecise information is investigated by using the evidence theory. First, the uncertain input parameters to be identified are approximately characterized by evidence variables with subinterval-type focal elements. Through the optimization procedure executed in the given computational model, the output response can be expressed as a group of interval numbers with basic probability assignment (BPA). In the subsequent inverse analysis framework, by cumulating the imprecise experimental response measurements with belief degrees to update the response BPAs, the related interval range of unknown evidence variables can be gradually calibrated toward the true value. To improve the optimization efficiency of output response calculation with respect to various focal elements, a relatively simple metamodel is established as an alternative of the original computational model, where the Legendre-type polynomial and Clenshaw-Curtis point are respectively utilized as the basis function and sample construction strategy. Eventually, numerical results in two examples verify that the uncertain parameter identification can be effectively achieved by the presented method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Joakim Beck, Lorenzo Tamellini, Raúl Tempone〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 28 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Jie Zhi, Tong-Earn Tay〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Composite structural failure usually entails complicated interactions between intralaminar and interlaminar damage. In this paper, a novel discontinuous solid-shell finite element combined with a 3D enriched cohesive element is formulated for the analysis of matrix cracking and delamination in multilayered composites. The proposed formulations are computationally attractive in modelling thin shell structures while retaining the advantages of solid elements. The bending performance was improved by using the enhanced assumed strain method and the assumed natural strain method, which alleviates potential locking problems. A linear elastic orthotropic law was used for layered shells and cracks therein were modelled with a cohesive zone model. A discrete crack method with floating nodes enriching the developed elements enables a mesh-independent description of ply cracks and their interaction with interface cracks. The applicability of the current formulation was verified with numerical examples including large deformations of thin shell problems and delamination growth in post-buckled laminates. Finally, the explicit and totally discrete modelling of matrix and delamination cracks in low velocity impact of cross-ply and angle-ply laminates was demonstrated. Numerical predictions of structural responses and damage patterns agree well with experimental results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 27 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Matthijs Langelaar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents a topology optimization approach that incorporates restrictions of multi-axis machining processes. A filter is defined in a density-based topology optimization setting, that transforms an input design field into a geometry that can be manufactured through machining. The formulation is developed for 5-axis processes, but also covers other multi-axis milling configurations, e.g. 2.5D milling and 4-axis machining by including the appropriate machining directions. In addition to various tool orientations, also user-specified tool length and tool shape constraints can be incorporated in the filter. The approach is demonstrated on mechanical and thermal 2D and 3D numerical example problems. The proposed machining filter allows designers to systematically explore a considerably larger range of machinable freeform designs through topology optimization than previously possible.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 25 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): S. Duczek, H. Gravenkamp〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An efficient and robust finite element-based transient analysis of structures is important in many engineering applications. In this context, a diagonal or lumped mass matrix is an essential prerequisite. In the last decades, several methods to construct such a mass matrix have been proposed and therefore a comprehensive and unbiased evaluation of these approaches in needed. In the present article, we consequently investigate established mass lumping schemes, such as the row-sum method and the diagonal scaling method, as well as the recently proposed manifold-based method. Furthermore, the latter approach is rigorously extended to higher order serendipity finite elements in two and three dimensions. Note that the manifold-based method and the diagonal scaling method are very general approaches, in the sense that they are applicable to arbitrary nodal-based shape functions with arbitrary polynomial orders, while guaranteeing the positive-definiteness of the lumped mass matrix. With respect to the row-sum method the positivity is not ensured and negative or zero diagonal components might be computed. Consequently, a detailed analysis of the influence and performance of these mass lumping schemes on the numerical results is conducted. To this end, several dynamic benchmark models (including modal, harmonic, and transient analyses) are selected, showing that only suboptimal rates of convergence are attained if serendipity finite elements based on a diagonal mass matrix are employed.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 24 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Jung Heon Song, Matthias Maier, Mitchell Luskin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene, at subwavelength distances. We construct an adaptive finite-element method to compute the ratio of energy transmitted within these waveguide structures reliably and efficiently. At its heart, the method is built upon a goal-oriented a posteriori error estimation with the dual-weighted residual method (DWR).〈/p〉 〈p〉Furthermore, we derive analytic solutions of the two-layer system, compare those to (known) single-layer configurations, and compare and validate our numerical findings by comparing numerical and analytical values for optimal spacing of the two-layer configuration. Additional aspects of our numerical treatment, such as local grid refinement, and the utilization of perfectly matched layers (PMLs) are examined in detail.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 30 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Marek Fassin, Robert Eggersmann, Stephan Wulfinghoff, Stefanie Reese〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In order to exclude spurious failure in compression the consideration of tension compression asymmetry (TCA) in damage models is of great interest in research as well as in industry. This paper presents an efficient and unifying algorithmic procedure for the incorporation of TCA into damage models. With the presented approach the implementation effort is drastically reduced since the equations and subroutines of the model without TCA can be reused. The strategy is first introduced and illustrated for an isotropic damage model. Afterwards, the procedure is applied to a gradient-extended anisotropic damage model with a second order damage tensor recently developed by the authors. For this model studies at integration point level as well as structural examples are presented. Two different aspects are included in the presented TCA approach and are demonstrated with the results of the simulations: (i) different damage evolution in tension and compression and (ii) stiffness recovery (crack closure) under compression. Due to the utilized gradient-extended formulation, being very efficient since only one additional degree of freedom is introduced, the finite element computations are shown to deliver mesh-objective results.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Julian Kochmann, Kiran Manjunatha, Christian Gierden, Stephan Wulfinghoff, Bob Svendsen, Stefanie Reese〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This work is concerned with the development of a novel model order reduction technique for FFT solvers. The underlying concept is a compressed sensing technique which allows the reconstruction of highly incomplete data using non-linear recovery algorithms based on convex optimization, provided the data is sparse or has a sparse representation in a transformed basis. In the context of FFT solvers, this concept is utilized to identify a reduced set of frequencies on a sampling pattern in the frequency domain based on which the Lippmann–Schwinger equation is discretized. Classical fixed-point iterations are performed to solve the local problem. Compared to the unreduced solution, a significant speed-up in CPU times at a negligibly small loss of accuracy in the overall constitutive response is observed. The generation of highly resolved local fields is easily possible in a post-processing step using reconstruction algorithms which are available as open source routines. The developed reduction technique does not require any time-consuming offline computations, e.g. for the generation of snapshots, is not restricted to any kinematic or constitutive assumptions and its implementation is straightforward. Composites consisting of elastic inclusions embedded in an i) elastic and ii) elastoplastic matrix are investigated as representative simulation examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): M.I. El Ghezal, L. Wu, L. Noels, I. Doghri〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61–112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy–Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): L. Carreras, E. Lindgaard, J. Renart, B.L.V. Bak, A. Turon〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Computing mode-decomposed energy release rates in arbitrarily shaped delaminations involving large fracture process zones has not been previously investigated. The 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si257.gif"〉〈mi〉J〈/mi〉〈/math〉-integral is a suitable method for calculating this, because its domain-independence can be employed to reduce the integration domain to a cohesive interface, and reduce it to a line integral. However, the existing formulations for the evaluation of the mode-decomposed 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si257.gif"〉〈mi〉J〈/mi〉〈/math〉-integrals rely on the assumption of negligible fracture process zones. In this work, a method for the computation of the mode-decomposed 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si257.gif"〉〈mi〉J〈/mi〉〈/math〉-integrals in three-dimensional problems involving large fracture process zones and using the cohesive zone model approach is presented. The formulation is applicable to curved fronts with non-planar crack faces. A growth driving direction criterion, which takes into account the loading state at each point, is used to render the integration paths and to decompose the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si257.gif"〉〈mi〉J〈/mi〉〈/math〉-integral into loading modes. This results in curved and non-planar integration paths crossing the cohesive zone. Furthermore, its implementation into the finite element framework is also addressed. The formulation is validated against virtual crack closure technique (VCCT) and linear elastic fracture mechanics (LEFM)-based analytical solutions and the significance and generality of the formulation are demonstrated with crack propagation in a three-dimensional composite structure.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Andrea Bartezzaghi, Luca Dedè, Alfio Quarteroni〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We consider the numerical approximation of lipid biomembranes at equilibrium described by the Canham–Helfrich model, according to which the bending energy is minimized under area and volume constraints. Energy minimization is performed via 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉-gradient flow of the Canham–Helfrich energy using two Lagrange multipliers to weakly enforce the constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembranes as single-patch NURBS closed surfaces. We discretize the geometric PDEs in space with NURBS-based Isogeometric Analysis and in time with Backward Differentiation Formulas. We tackle the nonlinearity in our formulation through a semi-implicit approach by extrapolating, at each time level, the geometric quantities of interest from previous time steps. We report the numerical results of the approximation of the Canham–Helfrich problem on ellipsoids of different aspect ratio, which leads to the classical biconcave shape of lipid vesicles at equilibrium. We show that this framework permits an accurate approximation of the Canham–Helfrich problem, while being computationally efficient.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): S. Klinkel, R. Reichel〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The contribution is concerned with a numerical element formulation in boundary representation. It results in a polynomial element description with an arbitrary number of nodes on the boundary. Scaling the boundary description determines the interior domain. The scaling approach is adopted from the so-called scaled boundary finite element method (SBFEM), which is a semi-analytical formulation to analyze problems in linear elasticity. Within this method, the basic idea is to scale the boundary with respect to a scaling center. The boundary, which is denoted as circumferential direction, and the scaling direction span the parameter space. In the present approach, interpolations in scaling direction and circumferential direction are introduced. The interpolation in circumferential direction is independent of the scaling direction. The formulation is suitable to analyze problems in nonlinear solid mechanics. The displacement degrees of freedom are located at the nodes on the boundary and in the interior element domain. The degrees of freedom located at the interior domain are eliminated by static condensation, which leads to a polygonal finite element formulation with an arbitrary number of nodes on the boundary. The element formulation allows per definition for Voronoi meshes and quadtree mesh generation. Numerical examples give rise to the performance of the present approach in comparison to other polygonal element formulations, like the virtual element method (VEM). Some benchmark tests show the capability of the element formulation. A comparison to standard and mixed element formulations is presented. The present approach is perfectly suitable to model heterogeneous structures with inclusions and voids. It avoids also staircase approximation of curved boundaries.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Thiago O. Quinelato, Abimael F.D. Loula, Maicon R. Correa, Todd Arbogast〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For meshes of nondegenerate, convex quadrilaterals, we present a family of stable mixed finite element spaces for the mixed formulation of planar linear elasticity. The problem is posed in terms of the stress tensor, the displacement vector and the rotation scalar fields, with the symmetry of the stress tensor weakly imposed. The proposed spaces are based on the Arnold–Boffi–Falk (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈msub〉〈mrow〉〈mi mathvariant="script"〉ABF〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈mi〉k〈/mi〉〈mo〉≥〈/mo〉〈mn〉0〈/mn〉〈/math〉) elements for the stress and piecewise polynomials for the displacement and the rotation. We prove that these finite elements provide full 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si17.gif"〉〈mi〉H〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi mathvariant="normal"〉div〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-approximation of the stress field, in the sense that it is approximated to order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si965.gif"〉〈msup〉〈mrow〉〈mi〉h〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈mo〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si958.gif"〉〈mi〉h〈/mi〉〈/math〉 is the mesh diameter, in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si17.gif"〉〈mi〉H〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi mathvariant="normal"〉div〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-norm. We show that displacement and rotation are also approximated to order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si965.gif"〉〈msup〉〈mrow〉〈mi〉h〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈mo〉+〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉 in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si935.gif"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈/math〉-norm. The convergence is optimal order for 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si993.gif"〉〈mi〉k〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉, while the lowest order case, index 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si10.gif"〉〈mi〉k〈/mi〉〈mo〉=〈/mo〉〈mn〉0〈/mn〉〈/math〉, requires special treatment. The spaces also apply to both compressible and incompressible isotropic problems, i.e., the Poisson ratio may be one-half. The implementation as a hybrid method is discussed, and numerical results are given to illustrate the effectiveness of these finite elements.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Jean-Luc Guermond, Bojan Popov, Ignacio Tomas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by the scheme. The method is formally first-order accurate in space. Then, we introduce a series of higher-order methods. When these methods violate the invariant domain properties, they are corrected by a limiting technique that we call convex limiting. After limiting, the resulting methods satisfy all the invariant domain properties that are imposed by the user (see Theorem 7.24) and is formally high-order accurate. The two key novelties are that (i) limiting is done by enforcing bounds on quasiconcave functionals; (ii) the bounds that are enforced on the solution at each time step are necessarily satisfied by the low-order approximation.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Judit Muñoz-Matute, Victor M. Calo, David Pardo, Elisabete Alberdi, Kristoffer G. van der Zee〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space–time domain. A full space–time variational formulation allows such representation. Most authors employ implicit time marching schemes to perform goal-oriented adaptivity as it is known that they can be reinterpreted as Galerkin methods. In this work, we consider variational forms for explicit methods in time. We derive an appropriate error representation and propose a goal-oriented adaptive algorithm in space. For that, we derive the forward Euler method in time employing a discontinuous-in-time Petrov–Galerkin formulation. In terms of time domain adaptivity, we impose the Courant–Friedrichs–Lewy condition to ensure the stability of the method. We provide some numerical results in 1D space + time for the diffusion and advection–diffusion equations to show the performance of the proposed explicit-in-time goal-oriented adaptive algorithm.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Manik Bansal, I.V. Singh, B.K. Mishra, S.P.A. Bordas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles) may intersect any given element (we call those elements multi-split elements). These discontinuities are modeled by imposing additional degrees of freedom at the nodes. The main advantage of the proposed scheme is that the mesh size remains independent of the relative distance among the heterogeneities/discontinuities. The pores and reinforcement particles are assumed to be spherical. The simulations are performed for uniform and non-uniform heterogeneity distribution. The Young’s modulus of the heterogeneous material is evaluated for different amount of pores and reinforcement particles. To demonstrate the computational efficiency of the multi-split XFEM, elastic damage analysis is performed for the unit cell with 5% pores and 5% reinforcement particles under uniaxial tensile loading. These simulations show that the Young’s modulus decreases linearly with the increase in the volume fraction of the pores and increases linearly with the increase in volume fraction of reinforcement particles. The multi-split XFEM is found to be at least 1.8 times computationally efficient than standard XFEM and at least 6.7 times computationally efficient than FEM.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Yaguang Wang, Zhan Kang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies concurrent two-scale design optimization of composite structures filled with multiple microstructural unit cells. The task of the design problem is to simultaneously optimize microstructural configurations of the unit cells and their spatial distribution in the macroscale. To this end, a new topology optimization framework based on combined topology representation of the density model and the level set model is proposed. The homogenization method is used to link the material microstructural design and the macroscale design by evaluating the effective properties of the microstructures. In the microscale, topology optimization of multiple microstructural unit cells is performed with the density-based method. In the macroscale design, the distribution of multiple microstructural unit cells is optimized by the velocity field level set method, which inherits advantages of the implicit geometrical representation of the conventional level set model (relatively clear and smooth material boundaries/interfaces, more natural description of topological evolution). Moreover, the velocity field level set method maps the variational boundary shape optimization problem into a finite-dimensional design space, thus making it relatively easy and efficient to employ general mathematical programming algorithms to handle the multiple constraints and two types of design variables in the concurrent two-scale design problem. Numerical examples show that the present concurrent two-scale design method can generate meaningful designs of hierarchical cellular structures with well-defined boundaries and material interfaces.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Elyes Ahmed, Florin Adrian Radu, Jan Martin Nordbotten〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with the analysis of coupled mixed finite element methods applied to the Biot’s consolidation model. We consider two mixed formulations that use the stress tensor and Darcy velocity as primary variables as well as the displacement and pressure. The first formulation is with a symmetric stress tensor while the other enforces the symmetry of the stress weakly through the introduction of a Lagrange multiplier. The well-posedness of the two formulations is shown through Galerkin’s method and suitable a priori estimates. The two formulations are then discretized with the backward Euler scheme in time and with two mixed finite elements in space. We present next a general and unified a posteriori error analysis which is applicable for any flux- and stress-conforming discretization. Our estimates are based on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mrow〉〈mo〉(〈/mo〉〈mi〉Ω〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉-conforming reconstruction of the pressure and a suitable 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈msup〉〈mrow〉〈mfenced open="[" close="]"〉〈mrow〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈mrow〉〈mo〉(〈/mo〉〈mi〉Ω〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/mrow〉〈/mfenced〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈/math〉-conforming reconstruction of the displacement; both are continuous and piecewise affine in time. These reconstructions are used to infer a guaranteed and fully computable upper bound on the energy-type error measuring the differences between the exact and the approximate pressure and displacement. The error components resulting from the spatial and the temporal discretization are distinguished. They are then used to design an adaptive space–time algorithm. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive algorithm.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Kyongmin Yeo, Youngdeok Hwang, Xiao Liu, Jayant Kalagnanam〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si15.gif"〉〈mi〉h〈/mi〉〈mi〉p〈/mi〉〈/math〉-inverse model to estimate a smooth, non-negative source function from a limited number of observations for a two-dimensional linear source inversion problem. A standard least-square inverse model is formulated by using a set of Gaussian radial basis functions (GRBF) on a rectangular mesh system with a uniform grid space. Here, the choice of the mesh system is modeled as a random variable and the generalized polynomial chaos (gPC) expansion is used to represent the random mesh system. It is shown that the convolution of gPC and GRBF provides hierarchical basis functions for the linear source inverse model with the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si15.gif"〉〈mi〉h〈/mi〉〈mi〉p〈/mi〉〈/math〉-refinement capability. We propose a mixed 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si567.gif"〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si422.gif"〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉 regularization to exploit the hierarchical nature of the basis functions to find a sparse solution. The 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si15.gif"〉〈mi〉h〈/mi〉〈mi〉p〈/mi〉〈/math〉-inverse model has an advantage over the standard least-square inverse model when the number of data is limited. It is shown that the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si15.gif"〉〈mi〉h〈/mi〉〈mi〉p〈/mi〉〈/math〉-inverse model provides a good estimate of the source function even when the number of unknown parameters (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si7.gif"〉〈mi〉m〈/mi〉〈/math〉) is much larger the number of data (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si8.gif"〉〈mi〉n〈/mi〉〈/math〉), e.g., 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si9.gif"〉〈mi〉m〈/mi〉〈mo〉∕〈/mo〉〈mi〉n〈/mi〉〈mo〉〉〈/mo〉〈mn〉40〈/mn〉〈/math〉.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 May 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 348〈/p〉 〈p〉Author(s): M. Li, J. Füssl, M. Lukacevic, J. Eberhardsteiner, C.M. Martin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉This paper presents a new adaptive strategy to efficiently exploit velocity discontinuities in 3D finite-element-based upper bound limit analysis formulations. Based on an initial upper bound result, obtained with a conventional approach without velocity discontinuities, possible planes of plastic flow localisation are determined at each strain-rate evaluation node and, subsequently, this information is used to sequentially introduce discontinuities into the considered discretised structure. During a few iterations, by means of introducing new and adjusting existing discontinuities, an optimal velocity discontinuity layout is obtained. For the general 3D case, the geometry of this layout is defined by the well-known level set method, standardly used to define the geometry of cracks in the extended finite element method.〈/p〉 〈p〉To make this method also applicable for orthotropic strength behaviours, traction-based yield functions defining the plastic flow across discontinuities are derived from their stress-based counterparts. This procedure is outlined in detail and the obtained traction-based yield functions are verified numerically, to guarantee a consistent strength behaviour throughout the whole discretised structure.〈/p〉 〈p〉By means of three different examples, including isotropic as well as orthotropic yield functions, the performance of the proposed strategy is investigated and upper bound results as well as failure modes are compared to reference solutions. The proposed approach delivers reliable upper bounds for each example and the majority of plastic flow takes place across the sensibly-arranged discontinuities. For this reason, very good upper bounds can be obtained with a quite coarse finite element mesh and only few introduced velocity discontinuities. This represents an attractive alternative to commonly-used adaptive mesh refinement strategies, where often a huge number of degrees of freedom need to be added to capture localised failure.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Minliang Liu, Liang Liang, Wei Sun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The patient-specific biomechanical analysis of the aorta requires the quantification of the 〈em〉in vivo〈/em〉 mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from 〈em〉in vivo〈/em〉 image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of 〈em〉in vivo〈/em〉 material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters is established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Jonathan B. Russ, Haim Waisman〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Structural topology optimization in the context of material degradation and fracture has been gaining considerable interest. In this work we explore the use of the phase field method for fracture in order to increase the fracture resistance, or strength, of a structure prior to failure by directly constraining the phase field approximation of the fracture surface energy. A density-based topology optimization framework is used and the total weight of the structure is minimized. The analytical sensitivities are derived and an efficiency gain based on the Schur-complement is presented for the computation of the sensitivities. The effectiveness of the proposed method is then demonstrated for two benchmark examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Matthias Faes, David Moens〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Classical (independent) interval analysis considers a hyper-cubic input space consisting of independent intervals. This stems from the inability of intervals to model dependence and results in a serious over-conservatism when no physical guarantee of independence of these parameters exists. In a spatial context, dependence of one model parameter over the model domain is usually modelled using a series expansion over a set of basis functions that interpolate a set of globally defined intervals to local (coupled) uncertainty. However, the application of basis functions is not always appropriate to model dependence, especially when such dependence does not have a spatial nature but is rather scalar. This paper therefore presents a flexible approach for the modelling of dependent intervals that is also applicable to multivariate problems. Specifically, it is proposed to construct the dependence structure in a similar approach to copula pair constructions, yielding a limited set of 2-dimensional dependence functions. Furthermore, the well-known Transformation Method is extended to the case of dependent interval analysis. The applied case studies indicate the flexibility and performance of the method.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 347〈/p〉 〈p〉Author(s): Alex Gorodetsky, Sertac Karaman, Youssef Marzouk〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of “continuous” matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Alessandro Tasora, Simone Benatti, Dario Mangoni, Rinaldo Garziera〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This work discusses an efficient formulation of a geometrically exact three-dimensional beam which can be used in dynamical simulations involving large displacements, collisions and non-linear materials. To this end, we base our model on the shear-flexible Cosserat rod theory and we implement it in the context of Isogeometric Analysis (IGA). According to the IGA approach, the centerline of the beam is parameterized using splines; in our work the rotation of the section is parameterized by a spline interpolation of quaternions, and time integration of rotations is performed using the exponential map of quaternions. Aiming at an efficient and robust simulation of contacts, we propose the adoption of a non-smooth dynamics formulation based on differential-variational inequalities. The model has been implemented in an open-source physics simulation library that can simulate actuators, finite elements, rigid bodies, constraints, collisions and frictional contacts. This beam model has been tested on various benchmarks in order to assess its validity in non-linear static and dynamic analysis; in all cases the model behaved consistently with theoretical results and experimental data.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Felix Meister, Tiziano Passerini, Viorel Mihalef, Ahmet Tuysuzoglu, Andreas Maier, Tommaso Mansi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Simulating complex soft tissue deformations has been an intense research area in the fields of computer graphics or computational physiology for instance. A desired property is the ability to perform fast, if not real-time, simulations while being physically accurate. Numerical schemes have been explored to speed up finite element methods, like the Total Lagrangian Explicit Dynamics (TLED). However, real-time applications still come at the price of accuracy and fidelity. In this work, we explore the use of neural networks as function approximators to accelerate the time integration of TLED, while being generic enough to handle various geometries, motion and materials without having to retrain the neural network model. The method is evaluated on a set of experiment, showing promising accuracy at time steps up to 20 times larger than the “breaking” time step, as well as in a simple medical application. Such an approach could pave the way to very fast but accurate acceleration strategies for computational biomechanics.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Guillem Barroso, Antonio J. Gil, Paul D. Ledger, Mike Mallett, Antonio Huerta〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new cost-effective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electro-magneto-mechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the ill-conditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Daniel Wicht, Matti Schneider, Thomas Böhlke〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉Computational homogenization schemes based on the fast Fourier transform (FFT) enable studying the effective micromechanical behavior of polycrystalline microstructures with complex morphology. In the conventional strain-based setting, evaluating the single crystal elasto-viscoplastic constitutive law involves solving a non-linear system of equations which dominates overall runtime. Evaluating the inverse material law is much less costly in the small-strain context, because the flow rule is an explicit function of the stress.〈/p〉 〈p〉We revisit the primal and dual formulation of the unit cell problem of computational homogenization and use state of the art FFT-based algorithms for its solution. Performance and convergence behavior of the different solvers are investigated for a polycrystal and a fibrous microstructure of a directionally solidified eutectic.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Stephen A. Vavasis, Katerina D. Papoulia, M. Reza Hirmand〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Cohesive fracture is among the few techniques able to model complex fracture nucleation and propagation with a sharp (nonsmeared) representation of the crack. Implicit time-stepping schemes are often favored in mechanics due to their ability to take larger time steps in quasistatic and moderate dynamic problems. Furthermore, initially rigid cohesive models are typically preferred when the location of the crack is not known in advance, since initially elastic models artificially lower the material stiffness. It is challenging to include an initially rigid cohesive model in an implicit scheme because the initiation of fracture corresponds to a nondifferentiability of the underlying potential. In this work, an interior-point method is proposed for implicit time stepping of initially rigid cohesive fracture. It uses techniques developed for convex second-order cone programming for the nonconvex problem at hand. The underlying cohesive model is taken from Papoulia (2017) and is based on a nondifferentiable energy function. That previous work proposed an algorithm based on successive smooth approximations to the nondifferential objective for solving the resulting optimization problem. It is argued herein that cone programming can capture the nondifferentiability without smoothing, and the resulting cone formulation is amenable to interior-point algorithms. A further benefit of the formulation is that other conic inequality constraints are straightforward to incorporate. Computational results are provided showing that certain contact constraints can be easily handled and that the method is practical.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 356〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: Available online 21 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): M.H. Abbasi, L. Iapichino, B. Besselink, W.H.A. Schilders, N. van de Wouw〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Many physical phenomena, such as mass transport and heat transfer, are modeled by systems of partial differential equations with time-varying and nonlinear boundary conditions. Control inputs and disturbances typically affect the system dynamics at the boundaries and a correct numerical implementation of boundary conditions is therefore crucial. However, numerical simulations of high-order discretized partial differential equations are often too computationally expensive for real-time and many-query analysis. For this reason, model complexity reduction is essential. In this paper, it is shown that the classical reduced basis method is unable to incorporate time-varying and nonlinear boundary conditions. To address this issue, it is shown that, by using a modified surrogate formulation of the reduced basis ansatz combined with a feedback interconnection and a input-related term, the effects of the boundary conditions are accurately described in the reduced-order model. The results are compared with the classical reduced basis method. Unlike the classical method, the modified ansatz incorporates boundary conditions without generating unphysical results at the boundaries. Moreover, a new approximation of the bound and a new estimate for the error induced by model reduction are introduced. The effectiveness of the error measures is studied through simulation case studies and a comparison with existing error bounds and estimates is provided. The proposed approximate error bound gives a finite bound of the actual error, unlike existing error bounds that grow exponentially over time. Finally, the proposed error estimate is more accurate than existing error estimates.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 19 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Jiangping Xu, Guillermo Vilanova, Hector Gomez〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Tumors promote the growth of new capillaries through a process called angiogenesis. Blood flows through these new vessels providing cancerous cells with nutrients. However, because tumor-induced vasculature is defective, blood flow is heterogeneous both in space and time. As a result, regional hypoxia and acidosis may appear, increasing the malignancy of the tumor. In this work, we developed a three-dimensional model to address the complex interplay between angiogenesis, tumor growth, nutrient distribution and blood flow. The model emphasizes three-dimensional geometry of the vascular network and integration with 〈em〉in vivo〈/em〉 imaging techniques by use of the phase-field approach. We show that our method allows computing directly on the photoacoustic imaging raw data, avoiding the mesh generation process, which is the usual bottleneck for integration of computational methods and imaging data. We present two- and three-dimensional results of the dynamics of vascular tumor growth coupled with blood flow within a time-evolving capillary network.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 15 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): P. Salinas, C.C. Pain, H. Osman, C. Jacquemyn, Z. Xie, M.D. Jackson〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Numerical solution of the equations governing multiphase porous media flow is challenging. A common approach to improve the performance of iterative non-linear solvers for these problems is to introduce artificial diffusion. Here, we present a mass conservative artificial diffusion that accelerates the non-linear solver but vanishes when the solution is converged. The vanishing artificial diffusion term is saturation dependent and is larger in regions of the solution domain where there are steep saturation gradients. The non-linear solver converges more slowly in these regions because of the highly non-linear nature of the solution. The new method provides accurate results while significantly reducing the number of iterations required by the non-linear solver. It is particularly valuable in reducing the computational cost of highly challenging numerical simulations, such as those where physical capillary pressure effects are dominant. Moreover, the method allows converged solutions to be obtained for Courant numbers that are at least two orders of magnitude larger than would otherwise be possible.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): Carrie A. Christensen〈/p〉

Description: 〈p〉Publication date: 1 December 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 357〈/p〉 〈p〉Author(s): 〈/p〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Jian-Ying Wu, Tushar Kanti Mandal, Vinh Phu Nguyen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Being able to seamlessly deal with complex crack patterns like branching, merging and even fragmentation, phase-field fracture/damage models are promising in the modeling of localized failure in solids. This paper addresses a phase-field regularized cohesive zone model (PF-CZM) for hydrogen assisted cracking based on our previous work on purely mechanical problems. Two distinct hydrogen enhanced decohesion mechanisms are dealt with by introducing various implicitly defined (via the crack phase-field) hydrogen-dependent softening laws. The resulting models are then numerically tested and compared against several benchmark examples. It is found that, though the PF-CZM gives different results regarding various decohesion mechanisms, the global responses are insensitive to both the mesh discretization resolution and the incorporated length scale parameter even in the presence of hydrogen.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Matthew Kasemer, Paul Dawson〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A finite element framework is presented in which grains within a polycrystalline microstructure are pre-discretized into lamellar regions that become candidates to deform by twinning. This enables the mapping of the motion due to twinning on geometrically proper regions. At some point in the loading of the polycrystal, a twin is triggered, at which point the nodes within a twin region are rapidly mapped to their twinned location, the region’s crystal lattice is reoriented, and the remainder of the body deforms by means of crystallographic slip to enforce mechanical equilibrium. The framework allows for both the onset of twinning and twin growth, and is intended to serve as a test bed for investigating models proposed for these phenomena. In this paper, the framework is described and simulations are performed to demonstrate its ability to handle the large, fast deformation of twinning within a targeted grain of a polycrystalline aggregate. Various simulations are performed, where the initial twin width and the point of twin activation in the loading history are parameterized. Deformation fields in and around the twinned region are inspected after a twinning event, and changes in local stress states are discussed in light of global and local energetic metrics.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Luan M. Vieira, Matteo Giacomini, Ruben Sevilla, Antonio Huerta〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 January 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 358〈/p〉 〈p〉Author(s): Alexandre This, Hernán G. Morales, Odile Bonnefous, Miguel A. Fernández, Jean-Frédéric Gerbeau〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Mitral regurgitation is one of the most prevalent valvular heart disease. Proper evaluation of its severity is necessary to choose appropriate treatment. The PISA method, based on Color Doppler echocardiography, is widely used in the clinical setting to estimate various relevant quantities related to the severity of the disease. In this paper, the use of a pipeline to quickly generate image-based numerical simulation of intracardiac hemodynamics is investigated. The pipeline capabilities are evaluated on a database of twelve volunteers. Full pre-processing is achieved completely automatically in 55 min, on average, with small registration errors compared to the image spatial resolution. This pipeline is then used to study the intracardiac hemodynamics in the presence of diseased mitral valve. A strong variability among the simulated cases, mainly due to the valve geometry and regurgitation specifics, is found. The results from those numerical simulations are used to assess the potential limitations of the PISA method with respect to different MR types. While the PISA method provides reasonable estimates in the case of a simple circular regurgitation, it is shown that unsatisfying estimates are obtained in the case of non-circular leakage. Moreover, it is shown that the choice of high aliasing velocities can lead to difficulties in quantifying MR.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 1 November 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Weisheng Zhang, Dingding Li, Pilseong Kang, Xu Guo, Sung-Kie Youn〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the present work, a new IGA-based MMV (moving morphable void) approach for structural topology optimization is developed. In this approach, the MMV-based topology optimization framework is seamlessly integrated into IGA by using TSA (trimming surface analysis) technique. Compared with existing works where TSA is also employed for topology optimization, the proposed approach provides a robust and flexible control of structural geometry/topology, and has the capability of preventing the occurrence of self-intersection and jagged boundaries in a straightforward manner. The newly developed method is also applied to topology optimization of shell structures, which are widely used in engineering applications. It is found that by using only a relatively small number of IGA-based elements, the present MMV and IGA-based method can obtain optimized shell structures with smooth boundaries with the same ease as for 2-D planar problems. Numerical examples are also provided to demonstrate the effectiveness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 31 October 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Jian-Ying Wu, Yuli Huang, Vinh Phu Nguyen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Despite the popularity in modeling complex and arbitrary crack configurations in solids, phase-field damage models suffer from burdensome computational cost. This issue arises largely due to the robust but inefficient alternating minimization (AM) or staggered algorithm usually employed to solve the coupled damage–displacement governing equations. Aiming to tackle this difficulty, we propose in this work, 〈em〉for the first time〈/em〉, to use the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to solve in a monolithic manner the system of coupled governing equations, rather than the standard Newton one which is notoriously poor for problems involving non-convex energy functional. It is found that, the BFGS algorithm yields identical results to the AM/staggered solver, and is also robust for both brittle fracture and quasi-brittle failure with a single or multiple cracks. However, much less iterations are needed to achieve convergence. Furthermore, as the system matrix is less reformed per increment, the quasi-Newton monolithic algorithm is much more efficient than the AM/staggered solver. Representative numerical examples show that the saving in CPU time is about factor 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈mrow〉〈mn〉3〈/mn〉〈mo linebreak="goodbreak" linebreakstyle="after"〉∼〈/mo〉〈mn〉7〈/mn〉〈/mrow〉〈/math〉, and the larger the problem is, the more saving it gains. As the BFGS monolithic algorithm has been incorporated in many commercial software packages, it can be easily implemented and is thus attractive in the phase-field damage modeling of localized failure in solids.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 March 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 360〈/p〉 〈p〉Author(s): Hugo Casquero, Xiaodong Wei, Deepesh Toshniwal, Angran Li, Thomas J.R. Hughes, Josef Kiendl, Yongjie Jessica Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff–Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refinement of regions where increased resolution is needed. The benefits of using ASTS to define shell geometries are at least two-fold: (1) The manual and time-consuming task of building a new mesh from scratch using the CAD geometry as an input is avoided and (2) 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si259.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉 or higher inter-element continuity enables the discretization of shell formulations in primal form defined by fourth-order partial differential equations. A complete and state-of-the-art description of the development of ASTS, including extraordinary points and T-junctions, is presented. In particular, we improve the construction of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si259.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉-continuous non-negative spline basis functions near extraordinary points to obtain optimal convergence rates with respect to the square root of the number of degrees of freedom when solving linear elliptic problems. The applicability of the proposed technology to shell analysis is exemplified by performing geometrically nonlinear Kirchhoff–Love shell simulations of a pinched hemisphere, an oil sump of a car, a pipe junction, and a B-pillar of a car with 15 holes. Building ASTS for these examples involves using T-junctions and extraordinary points with valences 3, 5, and 6, which often suffice for the design of free-form surfaces. Our analysis results are compared with data from the literature using either a seven-parameter shell formulation or Kirchhoff–Love shells. We have also imported both finite element meshes and ASTS meshes into the commercial software LS-DYNA, used Reissner–Mindlin shells, and compared the result with our Kirchhoff–Love shell results. Excellent agreement is found in all cases. The complexity of the shell geometries considered in this paper shows that ASTS are applicable to real-world industrial problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 March 2020〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 360〈/p〉 〈p〉Author(s): M. Dittmann, S. Schuß, B. Wohlmuth, C. Hesch〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A crosspoint modification for general 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" altimg="si1.svg"〉〈msup〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msup〉〈/math〉 continuous mortar coupling conditions is presented. In particular, we modify the extended mortar method as introduced in Schuß et al. (2019) and Dittmann et al. (2019) to deal with crosspoints as they arise in multi-patch geometries. This modification is constructed in such a way, that we decouple the Lagrange multipliers at the crosspoint to avoid a global coupling condition across all interfaces. Moreover, we recast the underlying B-Splines such that they preserve the higher order best approximation property across the interface and the crosspoint. A detailed investigation is presented in the context of second order thermal problems, fourth order Cahn–Hilliard and sixth order Swift–Hohenberg formulations.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Zhilin Han, Stein K.F. Stoter, Chien-Ting Wu, Changzheng Cheng, Angelos Mantzaflaris, Sofia G. Mogilevskaya, Dominik Schillinger〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): R. Biswas, A.S. Shedbale, L.H. Poh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A small deformation micromorphic computational homogenization framework for matrix–inclusion composites was recently presented in Biswas and Poh (2017), where standard continuum models at the micro-scale are translated consistently onto the macro-scale to recover a micromorphic continuum. In this contribution, the micromorphic framework is extended to the regime of significant geometrical and material nonlinearities. Following the small deformation framework, an additional degree of freedom is introduced to capture the influence of rapid fluctuations within a unit cell. In this contribution, we elaborate on the specific choice of decomposition for the kinematic fields, where certain higher-order modes are deliberately neglected. Several examples are considered to illustrate the influence of different higher-order modes, and how the corresponding size effect emerges naturally in the homogenized micromorphic model. In the regime of geometrical softening, the higher order term provides a regularizing effect to give mesh independent solutions, albeit with a stiffer response. A detailed discussion on this phenomenon is provided. The homogenization framework is implemented using a client–server based parallel processing algorithm to reduce the computational time. The excellent predictive capability and efficiency of the micromorphic approach are demonstrated with a mixed loading problem on a composite plate with non-uniform cross-section. Furthermore, the micromorphic solutions are shown to be independent of the choice of a unit cell.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Osvaldo L. Manzoli, Pedro R. Cleto, Marcelo Sánchez, Leonardo J.N. Guimarães, Michael A. Maedo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Hydraulic fracturing is a technique based on the injection of a viscous fluid at high pressure into an engineered well with the intention of initiating and propagating multiple fractures in a rock formation containing hydrocarbons to increase well-reservoir connectivity. This work proposes a framework to simulate the initiation and propagation of hydraulically induced fracture based on the Continuum Strong Discontinuity Approach (CSDA) and solid finite elements with high aspect ratio (HAR) in the context of conventional continuum constitutive (stress–strain) relationships (based on damage theory). The porous media considered here are deformable and the hydro-mechanical problem is solved in a fully-coupled manner. Full details about the proposed continuous approach to model hydraulic fractures are presented, including the finite element equations and their approximations. The new approach is validated against analytical and numerical solutions. Moreover, the influence of the dimensions of the HAR interface elements on the results is also investigated.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Keyan Li, Di Wu, Wei Gao, Chongmin Song〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A novel spectral stochastic isogeometric analysis (SSIGA) is proposed for the free vibration analysis of engineering structures involving uncertainties. The proposed SSIGA framework treats the stochastic free vibration problem as a stochastic generalized eigenvalue problem. The stochastic Young’s modulus and material density of the structure are modelled as random fields with Gaussian and non-Gaussian distributions. The basis functions, the non-uniform rational B-spline (NURBS) and T-spline, within Computer Aided Design (CAD) system are adopted within the SSIGA, which can eliminate geometric errors between design model and uncertainty analysis model. The arbitrary polynomial chaos (aPC) expansion is implemented to investigate the stochastic responses (i.e. eigenvalues and eigenvectors) of the structure. A Galerkin-based method is freshly proposed to solve the stochastic generalized eigenvalue problems. The statistical moments, probability density function (PDF) and cumulative distribution function (CDF) of the eigenvalues can be effectively obtained. Two numerical examples with irregular geometries are investigated to illustrate the applicability, accuracy and efficiency of the proposed SSIGA for free vibration analysis of engineering structures.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Innocent Niyonzima, Yang Jiao, Jacob Fish〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Shape memory materials have gained considerable attention thanks to their ability to change physical properties when subjected to external stimuli such as temperature, pH, humidity, electromagnetic fields, etc. These materials are increasingly used for a large number of biomedical applications. For applications inside the human body, contactless control can be achieved by the addition of electric and/or magnetic particles that can react to electromagnetic fields, thus leading to a composite biomaterial. The difficulty of developing accurate numerical models for smart materials results from their multiscale nature and from the multiphysics coupling of involved phenomena. This coupling involves electromagnetic, thermal and mechanical problems. This paper contributes to the multiphysics modeling of a shape memory polymer material used as a medical stent. The stent is excited by electromagnetic fields produced by a coil which can be wrapped around a failing organ. In this paper we develop large deformation formulations for the coupled electro-thermo-mechanical problem using the electric potential to solve the electric problem. The formulations are then discretized and solved using the finite element method. Results are validated by comparison with results in the literature.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Hongyang Cheng, Takayuki Shuku, Klaus Thoeni, Pamela Tempone, Stefan Luding, Vanessa Magnanimo〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy.〈/p〉 〈p〉The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density.〈/p〉 〈p〉As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young’s modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The 〈em〉a priori〈/em〉 particle configuration is obtained from 3D X-ray computed tomography images. The 〈em〉a posteriori〈/em〉 expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.〈/p〉 〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Christian Engwer, Patrick Henning, Axel Målqvist, Daniel Peterseim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of inseparable scales. We show how the method can be implemented in a fairly standard Finite Element framework and discuss its realization for different types of problems, such as linear elliptic problems with rough coefficients and linear eigenvalue problems.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Damien André, Jérémie Girardot, Cédric Hubert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The Discrete Element Method (DEM), also known as Distinct Element Method (DEM), is extensively used to study divided media such as granular materials. When brittle failure occurs in continuum such as concrete or ceramics, the considered media can be viewed as divided. In such cases, DEM offers an interesting way to study and simulate complex fracture phenomena such as crack branching, crack extension, crack deviation under coupled mode or crack lip closure with friction.〈/p〉 〈p〉The fundamental difficulty with DEM is the inability of the method to deal directly with the constitutive equations of continuum mechanics. DEM uses force–displacement interaction laws between particles instead of stress–strain relationships. Generally, this difficulty is bypassed by using inverse methods, also known as calibration processes, able to translate macroscopic stress–strain relationships into local force–displacement interaction laws compatible within DEM frameworks. However, this calibration process may be fastidious and really hard to manage.〈/p〉 〈p〉The presented work proposes to improve the Distinct Lattice Spring Model in order to deal with non-regular domains, by using Voronoi cells, which allow to completely fill the volume space of discrete domains. With this approach, the rotational effects must be included in the contact formulation, which enables the management of large rigid body rotations. This work also introduces a simple method to manage brittle fracture. Using non-regular domains avoids the cracks paths conditioning, and allows to reproduce quantitatively the Brazilian test, very popular in the rock mechanics community.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 11 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Kenneth Duru, Alice-Agnes Gabriel, Gunilla Kreiss〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we develop a provably energy stable discontinuous Galerkin spectral element method (DGSEM), approximating the perfectly matched layer (PML) for the three and two space dimensional (3D and 2D) linear acoustic wave equations, in first order form, subject to well-posed linear boundary conditions. First, using the well-known complex coordinate stretching, we derive an efficient un-split modal PML for the 3D acoustic wave equation, truncating a cuboidal computational domain. Second, we prove asymptotic stability of the continuous PML by deriving energy estimates in the Laplace space, for the 3D PML in a heterogeneous acoustic medium, assuming piece-wise constant PML damping. In the time-domain, the energy estimate translates to a bound for the solutions in terms of the initial data. Third, we develop a DGSEM for the wave equation using physically motivated numerical flux, with penalty weights, which are compatible with all well-posed, internal and external, boundary conditions. When the PML damping vanishes, by construction, our choice of penalty parameters yields an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate. Fourth, to ensure numerical stability of the discretization when PML is present, it is necessary to systematically extend the numerical fluxes, and the inter-element and boundary procedures, to the PML auxiliary differential equations. This is critical for deriving discrete energy estimates analogous to the continuous energy estimates. Finally, we propose a procedure to compute PML damping coefficients such that the PML error converges to zero, at the optimal convergence rate of the underlying numerical method. Numerical solutions are evolved in time using the high order Taylor-type time stepping scheme of the same order of accuracy of the spatial discretization. By combining the DGSEM spatial approximation with the high order Taylor-type time stepping scheme and the accuracy of the PML we obtain an arbitrarily accurate wave propagation solver in the time domain. Numerical experiments are presented in 2D and 3D corroborating the theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Abhishek Arora, Ajeet Kumar, Paul Steinmann〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a computational framework to obtain nonlinearly elastic constitutive relations of one-dimensional continua modeled as special Cosserat rods. The kinematics of the recently proposed 〈em〉Helical Cauchy–Born rule〈/em〉 is used to construct a family of six-parameter (corresponding to the six strain measures of rod theory) helical rod configurations which are subjected to uniform strain field along their arc-length. This uniformity along the rod’s arc-length results in the reduction of three-dimensional equations of elasticity to just the rod’s cross-section which further allows us to obtain the induced force, moment and stiffnesses of the rod by solving a nonlinear cross-sectional warping problem for every state of strain. The formulation is general in that the rod’s material could obey arbitrary three-dimensional hyperelastic constitutive relations. A nonlinear finite element formulation is presented to solve the cross-sectional warping problem and further obtain the induced force, moment and stiffnesses numerically. Several numerical examples are presented illustrating warping due to bending, shearing and torsion in rectangular as well as circular rods and how the warping affects stiffnesses. We also obtain all the stiffnesses of helically reinforced tubes and show the variation in their stiffnesses with the tube’s fiber angle.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 349〈/p〉 〈p〉Author(s): Changsheng Wang, Xiangkui Zhang, Guozhe Shen, Yang Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Isogeometric analysis (IGA) has been used with great success when combined with incremental methods to simulate sheet metal forming. In this paper, we present the development of one-step inverse IGA based on the total deformation theory of plasticity. For a large number of industrial stamping parts, the membrane effects are dominant. Thus, we adopted an isogeometric membrane element to predict the flattened contour of the initial blank from the energy-based initial solution estimation approach. In addition, we used the Newton–Raphson algorithm for nonlinear plastic iterations to evaluate the thickness and equivalent strain and stress of the final stamping parts. We applied our framework to square box and S-rail surface models for demonstration. The results for these two examples illustrate the performance of one-step inverse IGA and its applicability to the integrated design of sheet metal forming.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Shuwei Zhou, Xiaoying Zhuang, Timon Rabczuk〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A phase field model for fluid-driven dynamic crack propagation in poroelastic media is proposed. Therefore, classical Biot poroelasticity theory is applied in the porous medium while arbitrary crack growth is naturally captured by the phase field model. We also account for the transition of the fluid property from the intact medium to the fully broken one by employing indicator functions. We employ a staggered scheme and implement our approach into the software package COMSOL Multiphysics. Our approach is first verified through three classical benchmark problems which are compared to analytical solutions for dynamic consolidation and pressure distribution in a single crack and in a specimen with two sets of joints. Subsequently, we present several 2D and 3D examples of dynamic crack branching and their interaction with pre-existing natural fractures. All presented examples demonstrate the capability of the proposed approach of handling dynamic crack propagation, branching and coalescence of fluid-driven fracture.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): L. Roldán, J.J. Muñoz, P. Sáez〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉During the lifetime of all living multicellular organisms, wounds in their tissues are frequently observed. The capability of closing those gaps is fundamental for a healthy development. If done deficiently, many diseases may occur from simple inflammation to tumor formation. The wound healing process in epithelial tissue occurs in three different stages. The first one is the assembly of a supra-cellular actomyosin cable and its migration towards the wound edge, triggered by biochemical processes in which calcium plays a distinctive role. How this process is orchestrated following damage remains unclear. Later, after its positioning, the cable contracts driving the tissue towards the gap and reducing the wound area. Finally, cell migration towards the interior of the wound ends up sealing the tissue. In this work, we make use of a mechanical continuum model for the first two stages in order to developed and 2D finite element simulations within a monolithically fully implicit implementation. The model for the actomyosin cable formation involves the coupling of transient calcium ions transport, with actin fibers and myosin motors recruitment and non-linear mechanical response of the tissue. The contraction stage, the active deformation of the previously formed actomyosin cable is taken into account. The relative motion of the myosin motors over the actin filaments is modeled so there exists an active tissue contraction in the direction of those fibers. Upon implementation, the model is capable of performing a wide range of biophysical situations reported experimentally, as we demonstrate in our numerical results. We have been able to rationalize through computational mechanics the firing of calcium in the wound right after damage infliction as well as the consequent formation of actin ring, reproducing nicely what has been reported in biological literature. Thereafter, the numerical model of acto-myosin contraction, fully integrated with the non-linear mechanics of the problem, correlates with the mechanics of wound closure at the actin-ring contraction stage. More importantly, the approach is the first of its kind in the modeling of epithelial and embryonic cell layers, where a wide number of complex mechanics has been integrated and solved though computational methods in engineering. We believe that the simulations will help to unravel new insights in open questions of developmental biology.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 349〈/p〉 〈p〉Author(s): Bo Liu, Cuiyun Liu, Shuai Lu, Yang Wu, Yufeng Xing, A.J.M. Ferreira〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A differential quadrature hierarchical finite element method (DQHFEM) using Fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses. First, orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method (HFEM) were derived and simple formulas of transforming one dimensional non-uniform nodes to simplexes were presented. Then the non-uniform nodes were used as initial guesses to solve the Fekete points on simplexes through Newton–Raphson’s method together with the orthogonal polynomials. New differential quadrature (DQ) rules on simplexes were formulated using the HFEM bases and the Fekete points. The numbers of nodes or bases on different edges and faces and inside the body of the new DQ elements do not relate with each other like the HFEM that can freely assign different numbers of bases on different edges and faces and inside the body. So the new DQ method was named as a differential quadrature hierarchical (DQH) method that uses either interpolation functions or orthogonal polynomials as bases inside the element. Its weak form was named as the DQHFEM. Besides the DQH method and its weak form, a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single NURBS patch was presented. Numerical tests of the DQHFEM through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the DQH bases on both physical and geometric fields. It was concluded that wide applications of the DQH method and the DQHFEM to science and engineering are possible and commercial codes based on them are deserved to be developed.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 349〈/p〉 〈p〉Author(s): Tahsin Khajah, Vianey Villamizar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic waves. The ABC employed were recently devised by Villamizar et al. (2017) . They are derived from exact Farfield Expansions representations of the outgoing waves in the exterior of the regions enclosed by the artificial boundary. As a consequence, the error due to the ABC on the artificial boundary can be reduced conveniently such that the dominant error comes from the volume discretization method used in the interior of the computational domain. Reciprocally, the error in the interior can be made as small as the error at the artificial boundary by appropriate implementation of 〈em〉p-〈/em〉 and 〈em〉h〈/em〉-refinement. We apply this novel method to cylindrical, spherical and arbitrary shape scatterers including a prototype submarine. Our numerical results exhibit spectral-like approximation and high order convergence rate. Additionally, they show that the proposed method can reduce both the pollution and artificial boundary errors to negligible levels even in very low- and high-frequency regimes with rather coarse discretization densities in the IGA. As a result, we have developed a highly accurate computational platform to numerically solve time-harmonic acoustic wave scattering in two- and three-dimensions.〈/p〉〈/div〉

Description: 〈p〉Publication date: 1 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 349〈/p〉 〈p〉Author(s): Thuan Ho-Nguyen-Tan, Hyun-Gyu Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this study, a new polygonal shell element is developed to provide greater flexibility in mesh design of complex shell structures. Wachspress coordinates are used to construct shape functions for polygonal shell elements. An assumed covariant shear strain field with respect to the element natural coordinate system is defined by employing the mixed interpolation of tensorial components approach to avoid transverse shear locking in polygonal shell elements. Moreover, an assumed covariant membrane strain field is constructed by using characteristic geometry and displacement vectors defined on quadrilateral subdomains of polygonal shell elements to alleviate membrane locking due to the element curvature. Some benchmark shell problems are solved to evaluate the performance of the proposed polygonal shell elements. Numerical experiments show that they converge much better than triangular shell elements and comparable to quadrilateral shell elements.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Mark Ainsworth, Shuai Jiang, Manuel A. Sanchéz〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The Bernstein polynomials have been known for over a century and are widely used in the spline literature, computer aided geometric design, and computer graphics. However, the realisation that the Bernstein basis has favourable properties allowing the efficient implementation of high order methods for the approximation of partial differential equations is a relatively recent development. For instance, it is known Ainsworth et al. (2011) that the Bernstein basis can be exploited to compute all of the entries in the load vector in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 operations even in the case of non-linear problems on curvilinear elements for a degree 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si753.gif"〉〈mi〉p〈/mi〉〈/math〉 approximation. Moreover, the element matrices can be assembled in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 operations per entry. We show that properties of the Bernstein polynomials can also be exploited to obtain 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 complexity procedures for 〈em〉all〈/em〉 of the main components needed to implement a high order finite element code including: computation of the residuals needed for an iterative solution method; evaluating the action of a preconditioner for the global mass matrices; and, visualization and post-processing of the resulting finite element approximations.〈/p〉 〈p〉The construction of a preconditioner for the mass matrix whose condition number does not degenerate with the order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si753.gif"〉〈mi〉p〈/mi〉〈/math〉, at a cost of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 operations, is one of the main contributions of the present work. The preconditioner is based on an abstract Additive Schwarz Method recently developed by the authors. The preconditioner can be implemented at a cost of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 operations by exploiting properties of the Bernstein polynomials. In particular, we present an algorithm which allows one to invert the interior block of the element mass matrix in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉O〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈msup〉〈mrow〉〈mi〉p〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 operations. Numerical examples are provided to illustrate the applicability of the Bernstein basis to challenging non-linear reaction–diffusion problems, non-linear wave propagation of solitons and to robust approximation of problems exhibiting boundary layers.〈/p〉 〈/div〉

Description: 〈p〉Publication date: Available online 15 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): Michael Mengolini, Matías F. Benedetto, Alejandro M. Aragón〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this manuscript we study thoroughly the behavior of the virtual element method (VEM) in the context of two-dimensional linear elasticity problems. Through detailed convergence studies we show the accuracy and the convergence rates recovered by VEM, and we compare them to those obtained by the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si307.gif"〉〈mi〉h〈/mi〉〈/math〉– and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si292.gif"〉〈mi〉p〈/mi〉〈/math〉–versions of the finite element method (FEM). We also demonstrate the mixability between FEM and VEM; in particular, applications of VEM for coupling non-conforming discretizations and for local refinement are presented, showing higher versatility compared to FEM. Computer implementation aspects in displacement-based finite element codes are thoroughly explained, remarking on the main differences with respect to standard FEM.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 15 March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering〈/p〉 〈p〉Author(s): C. Ager, B. Schott, M. Winter, W.A. Wall〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The focus of this contribution is the numerical treatment of interface coupled problems concerning the interaction of incompressible fluid flow and permeable, elastic structures. The main emphasis is on extending the range of applicability of available formulations on especially three aspects. These aspects are the incorporation of a more general poroelasticity formulation, the use of the cut finite element method (CutFEM) to allow for large interface motion and topological changes of the fluid domain, and the application of a novel Nitsche-based approach to incorporate the Beavers-Joseph (-Saffmann) tangential interface condition. This last aspect allows one to extend the practicable range of applicability of the proposed formulation down to very low porosities and permeabilities which is important in several examples in application. Different aspects of the presented formulation are analyzed in a numerical example including spatial convergence, the sensitivity of the solution to the Nitsche penalty parameters, varying porosities and permeabilities, and a varying Beavers-Joseph interface model constant. Finally, a numerical example analyzing the fluid induced bending of a poroelastic beam provides evidence of the general applicability of the presented approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: 15 June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computer Methods in Applied Mechanics and Engineering, Volume 350〈/p〉 〈p〉Author(s): Lin Fu, Luhui Han, Xiangyu Y. Hu, Nikolaus A. Adams〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness of near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity.〈/p〉〈/div〉