ALBERT

Description: Volume 17 (2017) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 88 th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), held 6 – 10 March 2017 at Weimar, Germany, supported by Bauhaus-Universität Weimar and Technische Universität Ilmenau. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections Plenary Lectures PL Mechanics GAMM related DFG Priority Programmes PP01 Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis PP02 Reactive bubbly flows PP04 Calm, smooth and smart PP05 Non-smooth and complementarity-based distributed parameter systems: simulation and hierarchical optimization PP06 Polymorphic uncertainty modelling for the numerical design of structures PP07 Turbulent superstructures Minisymposia M 1 Innovative discretization methods, mechanical and mathematical investigations M 2 Recent trends in phase-field modelling M 3 Dislocation-based plasticity: State of the art and challenges M 6 Turbulent liquid metal and magnetohydrodynamic flows M 7 Flow Separation and vortical phenomena: Simulation in progress Sections 1–23 1 Multi-body dynamics 2 Biomechanics 3 Damage and fracture mechanics 4 Structural mechanics 5 Nonlinear oscillations 6 Material modelling in solid mechanics 7 Coupled problems 8 Multiscales and homogenization 9 Laminar flows and transition 10 Turbulence and reactive flows 11 Interfacial flows 12 Waves and acoustics 13 Flow control 14 Applied analysis 15 Uncertainty quantification 16 Optimization 17 Applied and numerical linear algebra 18 Numerical methods of differential equations 19 Optimization of differential equations 20 Dynamics and control 21 Mathematical signal and image processing 22 Scientific computing 23 Applied operator theory Young Researchers' Minisymposia YR 2 Computational techniques for bayesian inverse problems

Description: The notion of coherence in time-dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space. In particular, coherent behavior has an impact on transport and mixing processes in fluid flows. The mathematical definition and numerical study of coherent structures in flows has received considerable scientific interest for about two decades. However, mathematically sound methodologies typically require full knowledge of the flow field or at least high resolution trajectory data, which may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, such as obtained from particle tracking algorithms. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, in which Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph algorithms are then employed to analyze the resulting network. In particular, spectral graph partitioning schemes allow us to extract coherent sets of the underlying flow. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A hybrid dynamic substructuring method which combines experimentally measured and finite element (FE) modeled substructures in primal and dual form is presented. On the one hand, the model of the FE substructure is reduced to decrease the computational costs in the analysis of the hybrid model. On the other hand, the experimental substructure is measured while an instrumented fixture (known as Transmission Simulator) is assembled to its interface, providing the required interface dynamics for a high quality experimental model. The model of the transmission simulator is decoupled after measurement from the experimental substructure. Both the coupling and decoupling procedures are performed once with interface displacement (primal form) and once with interface forces (dual form). The hybrid substructuring methods are applied on an example and a comparison between both methods are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Using direct numerical simulations, we study the properties of turbulent superstructures in thermal convection in a large aspect ratio square cell. We estimate the characteristic length scale of superstructures using spatial auto-correlation functions and two-dimensional power spectra, and observe that the typical length scale increases weakly with increasing Prandtl number. We also find that the Prandtl number dependence of heat and momentum transport are similar to those observed in small aspect ratio systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present work, a three-dimensional discontinuous Galerkin (DG) formulation is presented and investigated for linear elastic problems, with special emphasis on locking phenomena. Among different variations of DG methods, the incomplete interior penalty Galerkin (IIPG) method is applied here, where the symmetry term is absent and the approach is stable through the application of a penalty term. Different examples are calculated to investigate the locking behavior of the DG method compared to continuous Galerkin (CG) method. Additionally, A locking-free 3D element formulation based on reduced integration and hourglass stabilization (Q1SP) is applied to compare and evaluate the results of the DG formulation in both shear and volumetric locking-dominated problems. Due to the discontinuity of the DG elements, a new meshing approach is applied in the finite element analysis program FEAP. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The understanding of NVH problems in brake systems becomes a strongly dominant remit in modern days. Finding solutions is the central task to achieve a calm and smooth system behavior. Brake squeal on automotive disk brakes represents a high frequency noise phenomenon resulting in potential customer complaints. The avoidance of squeal causes high costs in the automotive industry worldwide. One countermeasure for this disruptive noise issue is the application of thin composites named shims bonded to back plates of brake pads. The selection of appropriate shims is according to the state of the art still mainly based on trial and error. Current approaches seem to map the effects of shims on brake squeal insufficiently. To describe the shim behavior in an improved manner, prior experimental investigations have to be carried out, focusing on the identification of modal damping and stiffness values. The contribution shows experimental results of shims firmly bonded to brake pads and rectangular steel plates. Temperature variations and the analysis of nonlinearities like various excitation levels are examined in greater detail. As a result, the general influence of shims is presented and compared to measurements without damping materials. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Brake squeal is a self-excited vibration with initially inclining amplitude reaching a limit cycle due to nonlinearities. For a proper simulation of this behavior, it is necessary to know the origin and the influence of the brake system's nonlinearities. It is generally known, that nonlinearities are inherent to the joints [1, 2], complex friction laws [3] and the friction material of the system [4–6]. In this work, the influence of friction material and shim nonlinearities on the existence of a limit cycle is investigated. Stiffness and damping characteristics are determined using the chair's owned DCTR [4] test rig. It is shown, how nonlinear characteristics, which are necessary for simulation, are obtained from the performed measurements. They are incorporated in a multiple body model composed of brake disk, pads, shims, carrier and calliper from which the nonlinear equations of motion are derived. For the investigation on the bifurcation behavior, the equations of motion are transformed into normal form. It is then possible to describe the bifurcation behavior with respect to parameter influences. Ultimately, with this information it is possible to show the influence of the investigated nonlinearities on brake squeal. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: One research objective in the Priority Program 1897 “Calm, Smooth and Smart” of the German Research Foundation (DFG – SPP 1897) is the development of model order reduction techniques for parametric non-linear mechanical systems to enable efficient design, simulation, analysis, optimization and control of those. As a starting point for our research, this contribution provides an overview of the main challenges and well-established reduction techniques in this research area, at that stage, neglecting parameter dependencies. This includes simulation-based as well as simulation-free reduction bases generation and hyperreduction of the non-linear force terms. An extension of the Krylov directions in moment matching based on the concept of modal derivatives is also sketched. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Particle dampers are a promising alternative compared to conventional dampers due to their very flexible ability to dissipate energy in a wide frequency range even in rough environments. Simultaneously they cover additional functions like load bearing and noise reduction. For the understanding of particle dampers it is important to take into account the relevant physical phenomena which are interacting. The particles are modeled using the Discrete Element Method (DEM). Mesh-free methods such as the DEM pose to be appropriate in modeling large displacements of particle fillings in the damper and the dynamic contacts between adjacent particles resulting from high dynamics. In this work, a numerical experiment, where a particle damper is attached to a vertical leaf-spring, is set up to investigate the influence of typical parameters such as particle fill-ratios, particle size, and enclosure geometry on the damping performance of the particle damper. Moreover, the effect of an added liquid is also investigated. The Smoothed Particle Hydrodynamics (SPH) method is used in order to model the motion of the fluid. By using a coupled SPH-DEM approach, it is shown that complex interactions between particle-fillings, liquid, and enclosure geometry can be sufficiently well modeled. Thereby, it is possible to predict the influence of an added liquid on the vibration attenuation properties of the particle damper. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present study is devoted to the generalization of the Nonuniform Transformation Field Analysis (NTFA), a model-reduction approach introduced by the authors. First, the local fields of internal variables are decomposed on a reduced basis of modes. Second, the effective (average) dissipation potential of the phases is replaced by accurate approximations. The reduced evolution equations of the models, in other words the homogenized constitutive relations, can be entirely expressed explicitly in terms of quantities which are pre-computed “off-line”. The example of creep of polycrystalline ice is used to assess the accuracy of the models. Their predictions, both the overall response and the local response, are shown to be in good agreement with full-field simulations with a significant speed-up. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A framework for set-oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non-smooth objective functionals. Using an academic example, we show that the extension to non-smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For many engineering structures the dynamical response during operation is rarely stationary or regular. In fact, many studies on measured data reveal the irregular nature of dynamical system responses, for example in the field of research on brake squeal. Therefore, linear measures, such as amplitude and frequency spectra, cannot characterize the core dynamics contained in an irregular time series. Additionally, linear methods for damping extraction from measured signals tend to lose significance when it comes to irregular responses of self- excited systems. This work aims at highlighting the need for quantifiers from nonlinear time series analysis to adequately characterize real-world vibration data. In a first step a minimal model is studied to relate nonlinear time series quantifiers to internal system states and dissipation considerations. The goal of this research is to develop an understanding for the information contained in time series data concerning dissipation mechanisms of complex friction-excited systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Magnetic hybrid composite materials have the peculiarity to change their mechanical properties when influenced by a magnetic field. This special characteristic can be used to develop smart actuators, sensor systems and control mechanisms. In the paper the use of magneto-sensitive elastomers (MSE), composed of silicone rubber and silicone oil, with incorporated magnetic particles, in a form-fit gripper application is considered. The field-induced plasticity effect of MSE is used, to realise reversible recoverable shape adaptation of the gripper to the objects to be manipulated. The focus lies on the characterisation of the mechanical properties of the MSE for the specific application. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present paper we derive a reduced order model utilizing proper orthogonal decomposition (POD-ROM), for which we utilize adaptively obtained spatial snapshots. In a fully discrete setting this contains the challenge that the snapshots are vectors of different lengths. In order to handle this issue, we interprete the snapshots as elements of a common Hilbert space and consider the POD method from an infinite-dimensional perspective. Thus, the inner product of pairs of snapshots can be computed explicitely, which enables us to build the reduced order model. This approach is applied to a phase field model which is described by a Cahn-Hilliard equation. In the numerical examples we illustrate our appoach and compare a nonsmooth with a smooth free energy concerning the influence on the quality of the solution to the ROM. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Nowadays, numerical simulations enable the description of mechanical problems in many application fields, e.g. in soil or solid mechanics. During the process of physical and computational modeling, a lot of theoretical model approaches and geometrical approximations are sources of errors. These can be distinguished into aleatoric (e.g. model parameters) and epistemic (e.g. numerical approximation) uncertainties. In order to get access to a risk assessment, these uncertainties and errors must be captured and quantified. For this aim a new priority program SPP 1886 has been installed by the DFG which focuses on the so called polymorphic uncertainty quantification. In our subproject, which is part of the SPP 1886 (sp12), the focus is driven on quantification and assessment of polymorphic uncertainties in computational simulations of earth structures, especially for fluid-saturated soils. To describe the strongly coupled solid-fluid response behavior, the theory of porous media (TPM) will be used and prepared within the framework of the finite element method (FEM) for the numerical solution of initial and boundary value problems [2, 3]. To capture the impacts of different uncertainties on computational results, two promising approaches of analytical and stochastic sensitivity analysis will enhance the deterministic structural analysis [6–8]. A simple consolidation problem already provided a high sensitivity in the computational results towards variation of material parameters and initial values. The variational and probabilistic sensitivity analyses enable to quantify these sensitivities. The variational sensitivities are used as a tool for optimization procedures and capture the impact of different parameters as continuous functions. An advantage is the accurate approximation of the solution space and the efficient computation time, a disadvantage lies in the analytical derivation and algorithmic implementation. In the probabilistic sensitivity analysis from the field of statistics, the expense only increases proportionally to the problems dimension. Instead of a constant value, the model parameters are defined as probability distribution, which provides random values. Thus, a set of solution data is built up by several cycles of the simulation. Different approaches of the Bayes statistics will enable to receive accurate information with just a few simulations. The overall objective is the development of more efficient methods and tools for the sizing of earth structures in the long-run. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Herein, a finite strain microscale model for magnetorheological elastomers (MREs) based on a general continuum formulation of the magneto-mechanical boundary value problem is introduced. The modelling approach enables to consider particles with magnetically soft or magnetically hard behavior. In order to connect the microscopic fields to effective macroscopic quantities, a suitable computational homogenization scheme is used. The microstructure of the considered MRE is discretized and the problem is solved numerically in terms of a coupled nonlinear finite element approach. Using the presented framework, the influence of the particle shape on the magnetostrictive effect of MREs filled with magnetically soft particles is discussed. Furthermore, the effective macroscopic hystereses of an MRE filled with magnetically hard particles are calculated. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper concentrates on the aleatoric uncertainty of hyperelastic material models caused by material parameters which are characterized by random variables. To this end, the Polynomial Chaos Expansion (PCE) is applied to represent the random variables by a series of deterministic coefficients and random polynomials. To determine the corresponding PC coefficients and the polynomials of correlated stochastic material parameters we use the Cholesky decomposition and the Gram-Schmidt algorithm. Based on experimental results and artificial data parameter identification of an Ogden material model for rubber is applied. As a numerical example we consider a static problem for uniaxial tension of the rectangular plate. This structure is investigated in order to represent the conditions for the experimental setup. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This work considers the possibilistic interpretation of the fuzzy set theory for the fuzzy finite element method (FFEM). The underlying uncertainty type of design variables arises from sparse experimental data and is referred to as imprecise probability. In this context, a linear elastic body with given sparse experimental results for the design variables Young's modulus and Poisson's ratio is studied. To this end, the fuzzy input parameters are represented by possibility distributions generated by a probability-possibility transformation. A computational approach involving the α-level discretization technique [4] is applied in order to calculate the possibility of a quantity of interest. Finally, our method is applied in a numerical example for a plate with a ring hole. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Heterogeneous material properties can be found in new hybrid materials as well as in existing engineering constructions, e.g. dams. The material properties can be modeled by correlated random fields, taking into account their possible interdependencies. The vaguely known random field parameters like correlation coefficient and correlation length are described by fuzzy sets. Applying those fields in a reliability analysis result in failure probability fuzzy sets that can be interpreted by the engineer. This proposed methodology is applied to a simple illustrative one-dimensional model to show the principle procedure. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Phase-field methods for brittle fracture employ a variational framework and have proven to predict complex fracture patterns in two and three dimensional examples. This contribution focuses on a phase-field approach for a coupled field model of brittle pneumatic fracture. Two different challenges are tackled in this contribution: First, we have to deal with pressure-driven processes within the proposed phase-field ansatz, second, we have to consider the numerical effort of the simulations. Our phase-field formulation is based on elasticity and a suitable operator split to take only the tensile parts into account. Furthermore, a prescribed pressure is coupled with the phase-field parameter to consider crack propagation induced by pneumatic pressure. To keep the numerical effort as small as possible we apply a specifically developed multigrid method for three-dimensional problems. The accuracy and the robustness of the solution method will be demonstrated with a series of numerical examples. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this work, a hybrid discontinuous Galerkin (dG) quadrilateral element formulation is investigated. In hybrid formulations, the elements' interior is treated independently from the skeleton (the element boundaries). The global degrees of freedom (dofs) are located on the element corners. This makes the implementation into existing finite element codes simple. The dofs in the element interior are condensed out. The deformation gradient is taken homogeneous within the element instead of using bilinear shape funcitons. The result is a very simple formulation and numerical implementation. The element has been shown to be free of volumetric locking and shear locking. Moreover, the mesh convergence is close to well-known formulations like the Q1E4-, Q1P0- or Q1SP-element. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A general procedure for the treatment of uncertain, fuzzy-valued constraints in optimization problems is derived by considering the connection between fuzzy set theory and possibility theory, inspired by the results for chance-constrained programming in a fuzzy environment [1]. The proposed algorithm is exemplarily applied to synthesizing a controller for an uncertain system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Volume-locking is a significant problem when using the standard Finite Element Method (FEM) since this phenomenon can lead to failure of a numerical method. To circumvent constraints as related in (nearly) incompressible materials the novel discontinuous Petrov-Galerkin (dPG) FEM is introduced for linear elasticity. A first result of the implemented primal dPG FEM is shown for a patch test. Further tests on the performance of the proposed method are work in progress and are not part of this contribution. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This study presents a phase-field approach for an anisotropic continuum to model fracture of biological tissues and fiber-reinforced composites. We start with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler–Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the anisotropic crack phase-field and the balance of linear momentum. In addition, we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step and a crack evolution step. Representative numerical examples are devised for crack initiation and propagation in carbon-fiber-reinforced polymerg composites. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results qualitatively capture the effect of anisotropy in stiffness and strength. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A phase field model for elastic-plastic fracture is presented, which is based on an energy functional composed of an elastic energy contribution, a plastic dissipation potential and a fracture energy. The coupling of the mechanical fields with the fracture field is modeled by a degradation function. Due to the proposed coupling it is possible to solve the global system of differential equations in a monolithic iterative solution scheme. Numerical simulations are presented, where the choice of the degradation function is investigated and a staggered is compared to monolithic iteration scheme. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the fields of mechanical engineering, friction is ubiquitous. It is a fundamental cause of energy loss and wear. Another concern is the occurrence of comfort-relevant friction induced vibrations. Prominent examples of this are NVH phenomena such as brake squeal, which is being investigated at great expense by the German automotive industry and academia, to determine its causes and potential influencing factors. For this purpose, numerous specialized measurements are performed, and models of varying complexity are used. All of these measurements and models have the common trait that the coefficient of friction (COF), defined as the ratio of the tangential force and normal force, has a decisive influence on the systems' stability. To parameterize the friction coefficient in macroscopic models, measurements must be performed. In this case, often an average value over time and over various loading procedures is used. As the measurements reveal, the coefficient of friction is in reality not constant, but is subject to a high degree of dynamics on various time scales, caused by complex processes in the boundary layer. A treatment of the coefficient of friction as a steady-state parameter, or even as a constant, is thus a major reduction. The large variability of the coefficient of friction causes a corresponding variance in the stability limits of the models considered. This phenomenon is observed in the real world, where squealing seems to have a non-deterministic behavior. This suggests uncertainties in the modeling of the friction coefficient. Due to the various types of uncertainty (variability, incompleteness and inaccuracy), the entire problem is a matter of polymorphic uncertainty. This paper focuses on the modeling of the friction coefficient, taking into account the various causes of uncertainty. Selections of raw data obtained at the authors institute throughout many years of research on friction phenomena in brake systems will be evaluated and classified with respect to its uncertainty properties. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Many real world problems need simplifications in such a way that computing is reduced for answering specific questions, for example, to quantify uncertainties. Therefore so-called metamodels or surrogate models are developed which are based on interpolation or approximation methods. In this paper we transform the usual approximation or interpolation problem into a variational form such as it is known from the Finite Element method (FEM). With this variational framework it is possible to derive error estimators, which can be used later on for adaptivity. To compute the coefficients of the metamodel one needs some quadrature rules, which should be related to the given data. A numerical example shows the advantages of our proposed methods. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The effects of buoyancy on vertical duct flows with one heated side wall are investigated by means of Direct Numerical Simulations. In particular, the flow through square ducts and behind the expansion of a backward-facing step with side walls are presented for the forced and mixed convection regime. These configurations allow studying the interaction of buoyancy forces with secondary flow of second kind in the square duct and with the shear layer and recirculation zone in case of the expansion. In both configurations, buoyancy substantially alters the mean flow field, the turbulent stresses, and the heat transfer compared to the corresponding forced convection cases. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Even though many studies have been conducted to understand and model the passive response of arteries, very few studies have been performed to develop constitutive equation for the active response of arteries and to perform numerical simulations. In this paper, the diffusion of the neurotransmitter, for example noradrenaline, is combined with the anisotropic constitutive model to describe the temporal contraction of the smooth muscle cells in the artery wall. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Understanding functional principles of frost-resistant plant tissues under frost conditions is considered as an important milestone with regard to frost damage prevention in construction materials, as plant tissues are capable to withstand many freezing and thawing cycles without any damage. This contribution introduces a modelling approach for the biological role model based on the Theory of Porous Media (TPM) with an emphasis on structural properties and the phase transition of extracellular water. The presented numerical examples show the ice formation, represented by a frost front, where also structural effects of the plant's microstructure, such as inhomogeneity, can be considered in a numerical investigation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The current contribution deals with the simulation of the viral entry into a cell. There are two dominant mechanisms typical of this process: the endocytosis and the fusion with the cellular membrane. However, we only focus on the first scenario. To this end, we consider a virus as a substrate with a constant concentration of receptors on the surface. Opposite to this, the concentration of receptors of the host cell varies and these receptors are free to move over the membrane. When the contact with the cell surface has been achieved, the receptors start to diffuse to the contact (adhesion) zone. The membrane in this zone inflects and forms an envelope around the surface of the virus. This is the way the newly formed vesicle imports its cargo into the cell. In order to simulate the process described, we assume that the differential equation typical of the heat transport is suitable to simulate the diffusion of receptors. We also formulate two boundary conditions: First, we consider the balance of fluxes on the front of the adhesion zone. Here, it is supposed that the velocity is proportional to the gradient of the chemical potential. The second subsidiary condition is the energy balance equation depending on four different contributions: the energy of binding receptors, the free energy of the membrane, the energy due to the curvature of the membrane and the kinetic energy due to the motion of the front. The differential equation itself along with two boundary conditions forms a well-posed problem which can be solved by applying a direct method, for example the finite difference method. The contribution also includes numerical examples showing the distribution of receptors over the membrane as well as the motion of the front of the adhesion surface. The influence of the mobility of receptors has been studied in particular. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Finite element (FE) method simulations are increasingly used for the development in the area of vehicle safety nowadays. Highly detailed virtual mechanical and human body models (HBMs) available for use in connection with the increase of the processors performance and algorithms efficiency, give engineers the opportunity to simulate not only the car crash event itself but also a so-called pre-crash phase. This is important for the design and improvement of steering-assist and autonomous driving systems, through the assessment of active occupant behaviour during the impact avoidance or any other complex driving manoeuvres. To enable adequate evaluation of such simulations, virtual Active Human Body Models (AHBMs) should be established, capable to not only reproduce reflex human reactions but also for simulations of human movements. This study investigates the applicability of a forward dynamics movement generation algorithm for the FE HBMs, presents first results and outlines questions, need to be solved in future to do such simulations in a robust and time effective way. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The aim of the study presented here, is to understand and characterize the air puff generated by a non-contact tonometer (NCT). Therefore, we propose a method to experimental calibrate a computational fluid dynamic (CFD) model of an eye examined with a Corvis ST. The time dependence of the nozzle pressure was found to be equal to the pressure measured by a device intern sensor. However, the maximum pressure identified at the nozzle inlet reaches approximately 25 kPa. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this study, a workflow is presented for a personalized simulation of a bone–implant–system of a fractured tibia during a step forward. The workflow is based on routinely acquired tomographic data, segmentation, material assignment, mesh generation, setup of realistic boundary conditions and a finite element simulation (FEM). In the absence of patient–specific monitoring data, a dataset from the OrthoLoad database is implemented as individualized boundary conditions. This allows a simulation of the bone–implant–system close to reality of patient's step forward. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Animals, e.g. rats and cats, have different types of tactile hairs. One type are the mystacial vibrissae. They are located around the snout and in combination with the follicle-sinus complex they are powerful tactile sensors. With them, animals are able to detect the distance to an object, recognize the object shape and determine the surface texture. Adapting the natural example, the goal is to design an artificial tactile sensor with a similar functionality. In the course of this, a model for surface texture detection is developed. The vibrissa is modeled as an Euler-Bernoulli bending beam, incorporating large deflections. The contact, between vibrissa and surface, is modeled using Coulomb's law of friction. The mechanical modeling results in a nonlinear, system of first order differential equations. Solving the boundary-value problem by applying a shooting method, a quasi-static simulation is performed. Some first relations between the vibrissa morphology and the surface contact are analyzed. With view to an artificial sensor, the change of the reaction forces and moments at the base of the vibrissa due to the surface contact is the point of focus. Out of the reaction forces, the coefficient of static friction between vibrissa and surface is determined. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Heat transport in biological tissues and its modelling with different approaches, such as Pennes's bioheat equation and porous media theories, is investigated in this study. Breast cancer detection is envisaged as an application. The suitability of the widely-used Pennes model for breast cancer detection by means of infrared imaging is investigated through experimental and numerical examples. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present paper describes a simplified model for isotropic damage developed on continuum damage theory. The model characterizes the distinct behaviour of concrete in tension and compression using a unified equivalent strain, which governs the growth of damage. In reality, concrete exhibits distributed micro-cracking pattern under multi-directional loads. Therefore, the model is extended to incorporate damage induced anisotropy inherently for a reliable representation of damage, and captures the direction of possible damage evolution. Moreover, the model takes the inelastic behaviour of material into account based on the extended version of Lubliner failure criterion. The model is validated with experimental data. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present study, a semi-analytical asymptotic approach is used in order to analyse the change of total potential energy due to the initiation of a crack at a sharp re-entrant corner. The semi-analytical solution nature allows for reducing the numerical effort compared to a purely numerical treatment and provides a deeper physical insight into the fracture mechanics problem. Finally, the obtained asymptotic solutions are compared to numerical reference solutions. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present contribution is concerned with an experimental investigation of fatigue crack initiation in polycrystalline metals using a micro scale specimen testing technique. Based on the results of the experimental investigation and a fractographic investigation, a probabilistic microscale simulation procedure for prediction of the fatigue crack formation phase is proposed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Different mechanical processes induce a directional microstructure (texture) during the production of a material, e.g. during the hot rolling of aluminum plates or the injection molding process of natural fiber reinforced bio-polymers. In such materials the anisotropic mechanical features are related to the texture and have a decisive impact on the fracture process. Rolling or shot peening processes, on the other hand, induce an irreversible plastic deformation and residual compressive stresses for the purpose of a surface toughening. Similarly, residual stresses are induced if a circular core with interference fit is inserted into a drilled hole. The measurement of crack paths in specimens with residual stresses due to a core reveals an influence of the core's interference with respect to the crack deflection and the resulting paths [1,2]. Numerical investigations of fatigue crack growth show that conventional crack deflection criteria are not valid in such specimens, as the deflection angle depends on the magnitude of the external loading, going along with a rotation of the principal stress axes and thus the J k -vector [2]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The development of the typical hexagonal pattern of solidifying volcanic material can be described by fracture mechanics. While following the moving inhomogeneous temperature field, these columns reach a steady growth with a certain diameter. This spacing increases sometimes instantaneously. Using a bifurcation analysis based on the free Helmholtz energy this phenomenon is investigated and presented with this contribution. In order to handle the complex three-dimensional geometry, regularity in the pattern and a Fourier series expansion of the crack contour are used. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Phase-field models constitute a powerful tool in fracture mechanics. However, the main issues of these types of methods are the selection of the phase-field model parameters, the numerical requirement of very finely meshed structures, and extremely small integration time steps. The subject of this work is the construction of an artificial neural network representing a finite element model coupled with a phenomenological phase-field approach for brittle fracture. The approach is demonstrated on a notched plate in 2D. The neural network results and computation time is compared to established phase-field models. After an initial training process, the neural network is able to predict the response of the complex system in a fraction of the time compared to the non-local continuum mechanical model. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Nanocomposites exhibit excellent fracture toughness due to adding nanoparticles into the polymer matrix. The present work aims at developing a multiscale modelling approach to investigate fracture behaviour of nanocomposites with core-shell nanostructures. In this context, a nonlocal damage model based on the micropolar theory is proposed to describe the damage behaviour of graded shell layers of nanoparticles. The simulation results show the capability of the present model to study the effect of shell morphology and shell material on the fracture toughness of nanocomposites within this multiscale simulation framework. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The major function of the urinary bladder is the storage and release of urine. Undergoing large deformations while keeping the chemically aggressive urine and maintaining a relatively constant pressure during filling, the bladder shows remarkable mechanical properties. Those properties are based on the highly complex structure of the bladder wall. However, irregularities within the bladder wall may have negative implications on the correct functioning. In order to improve the understanding of different physiological processes taking place within the bladder wall during bladder filling and contraction, a computation tool is presented based on a continuum mechanics approach. In that sense the model is applied to complex boundary value problems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A major issue concerning Carbon Fibre Reinforced Polymer (CFRP) materials under cyclic loading is that the materials often undergo material degradation starting from the initial stage of the loading. For a laminate that consists of different fibre orientation plies, this becomes crucial as it causes redistribution of stresses and strains during the lifetime of the component. Understanding the importance of a reliable fatigue damage and degradation model in the development of reliability assessment of CFRP materials, the present studies contribute to this by considering the effect on a single-ply material level, exclusively under fatigue loading. The model is restricted to be applied to stiff and brittle materials with characteristic properties similar to those of carbon-epoxy composites. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The underlying research work aims to develop a numerical model of pressure-driven fracturing of saturated porous media. This is based on the combination of the phase-field modelling (PFM) scheme together with a continuum-mechanical approach of multi-phase materials. The proposed modelling framework accounts for the crack nucleation and propagation in the solid matrix of the porous material, as well as the fluid flow change in the cracked region. The macroscopic description of the saturated porous material is based on the theory of porous media (TPM), where the proposed scheme assumes a steady-state behaviour (quasi-static) and neglects all thermal and chemical effects. Additionally, it assumes an open system with possible fluid mass production from external source. Special focus is laid on the description of the interface and change of the volume fractions and the permeability parameter between the porous domain and the crack. Finally, a numerical example using the finite element method is presented and compared with experimental data to show the ability of the proposed modelling strategy in capturing the basic features of hydraulic fracturing. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The Dresden sodium facility for dynamo and thermohydraulic studies (DRESDYN) is a platform for large-scale liquid sodium experiments devoted to fundamental geo- and astrophysical questions as well as to various applied problems related to the conversion and storage of energy. Its most ambitious part is a precession driven dynamo experiment, comprising 8 tons of liquid sodium supposed to rotate with up to 10 Hz and to precess with up to 1 Hz. Another large-scale set-up is a Tayler-Couette experiment with a gap width of 0.2 m and a height of 2 m, whose inner cylinder rotates with up to 20 Hz. Equipped with a coil system for the generation of an axial field of up to 120 mT and two different axial currents through the center and the liquid sodium, this experiment aims at studying various versions of the magnetorotational instability and their combinations with the Tayler instability. We discuss the physical background of these two experiments and delineate the present status of their technical realization. Other installations, such as a sodium loop and a test stand for In-Service-Inspection experiments will also be sketched. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The high demand for physically-based continuum models of plasticity has induced renewed efforts to formulate continuum theories of dislocation kinematics and dynamics. Considering a dislocation density based model incorporating a set of evolution equations for arbitrary curved dislocation lines, the kinetic formulation of a velocity law of dislocation motion including dislocation interaction between different slip systems is investigated. Two short-range interaction terms accounting for forest interactions are comparatively discussed and differences are pointed out. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Biopolymer gels have many applications in tissue engineering. In recent years, biopolymer gels are widely used as scaffold material in the 3D bioprinting technique for tissues and organs. To optimise the printing process, it is important to study and understand the temperature- and time-dependent gelation kinetics of biopolymer gels. In this study, a thermodynamic model is proposed to describe the gelation kinetics of thermoreversible gels, which are driven by the coil-to-helix transition. In this model, the gelation process is assumed to proceed in two steps. The process starts from the reference state, in which the solution consists of solvent molecules and polymer chains with n segments in random coil configuration. Polymer chains firstly change from the random coil state to the partially helical state, followed by the aggregation of helical parts of polymer chains. This formation and the followed aggregation of helices lead to the eventual polymer network. With the help of the phase-field method, numerical simulations of a spatial and time varied gelation process of droplets in 3D bioprinting are performed using the finite element method (FEM). (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The effect of sudden amplitude changes of a spanwise traveling surface wave on turbulent boundary layers is investigated numerically using high resolution large-eddy simulation (LES). The results show drag reduction of up to 9 percent and an adaptation of the turbulent flow to the changed input parameter within 100 convective times. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Classic hybrid computational fluid dynamics - computational aeroacoustics simulations rely on disk I/O to exchange large volumes of data between the flow solver and the aeroacoustics solver, which considerably limits the scalability of the overall scheme. A direct-hybrid method is presented that eliminates this restriction by executing both solvers simultaneously on a joint hierarchical Cartesian mesh. Simulation results for a pair of co-rotating vortices show the parallel efficiency of the approach. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Liquid metal flows in the presence of a uniform magnetic field experience electromagnetic induction. The eddy currents and associated Lorentz force density modify the flow and give rise to thin electromagnetic boundary layers on the walls of the channel or duct. Hartmann layers develop on the walls perpendicular to the magnetic field whereas side layers develop on the parallel walls. The structure of the laminar flow depends on the conductivity of the walls. The side layers play a critical role in the transition to turbulence and are also strongly affected by the anisotropic character of the Lorentz force. We focus on duct flows with conducting Hartmann walls that give rise side-layers jets and report numerical studies of the transitional and turbulent regimes. We also examine one-point statistics and describe specific transitional patterns. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the mass conservation and geometry intersection of overset grid coupling strategies. The interpolation based grid coupling of the overset procedure violates the inherent mass conservation of finite-volume methods. This is problematic since incompressible finite-volume solvers directly use the mass defect when solving for the pressure. Furthermore, overset grid coupling requires a sufficient overlap for the interpolation of field values. Geometry intersection can be handled by an immersed boundary method. Applications refer to a collision simulation of two cylinders and the wall influence on the added mass of a cylinder. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The question how the brain controls locomotion is a highly treated one. This topic is taken up in this study by means of human computational models, simulating the human musculoskeletal system actuated by advanced Hill-type muscle models. A forward dynamic approach is considered allowing to simulate human motion independently from pre-measured trajectories and enabling to resemble the control of the central nervous system – the motor command selection. It is suggested that movement paths arise implicitly through optimisation [1,4]. Hence, stimulation patterns passing through activation dynamics are determined by means of constrained optimal control problems with physiologically motivated objective functions. One advantage concerning the implementation within Neweul-M 2 is the possibility to apply well-elaborated and tested optimisation algorithms available with Matlab to solve optimal control problems, enabling to employ the novel non-linear model predictive control (NMPC). The introduced framework is applied to treat different biomechanical movement scenarios including reaching scenarios of the arm which are validated against experimental data from [2–4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Liquid metal blankets will be tested in the experimental fusion reactor ITER. Three main concepts are currently under development. In the water-cooled and in the helium-cooled lead lithium blankets the PbLi alloy serves only as breeder material for producing the fuel component tritium used to generate the magnetically confined fusion plasma. The fusion heat is removed by a separated water or helium cooling system and therefore the liquid-metal could be practically at rest. However, for tritium extraction and liquid metal purification a weak circulation (1 mm/s) is required. Instead in the dual coolant lead lithium blanket the liquid metal serves both to produce tritium and to remove the volumetric heat deposited in the breeding zone, while helium is employed to cool first wall and blanket structure. In this concept PbLi has to flow faster (10 cm/s) than in the separately cooled blanket designs to allow efficient cooling of the breeding zone. In all liquid metal blankets there are issues related to the specific characteristics of the liquid metal. The interaction of the electrically conducting fluid with the strong magnetic field induces electric currents and electromagnetic forces that influence velocity and pressure distribution in the blanket. Lorentz forces are balanced by pressure gradients and these additional magnetohydrodynamic (MHD) pressure losses are proportional to the electric current density induced in the fluid. The electrical coupling of adjacent fluid domains that results from the presence of leakage currents crossing common conducting walls, has also to be taken into account. Two examples of MHD flows typical in fusion blankets are discussed in this paper. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, we derive and compare three integrators for nonsmooth mechanical systems by discretizing the principle of virtual action with finite elements in time. The weak as well as the strong variational form of the principle are discretized using a piecewise linear shape function and different quadrature rules. After introducing a suitable constitutive law for the contact forces arising in the discretized system, this approach leads to the well established time-stepping scheme of Moreau [1], the variational Moreau-type scheme derived in [3] and another related scheme, which we call the symmetric Moreau-type scheme. It is shown using a benchmark system that the symmetric and the variatonal Moreau-type schemes, in contrast to Moreau's scheme, show an excellent longterm energy behavior. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An approach to minimize the control costs and ensuring a stable deviation control is the Riccati controller and we use it to control constrained dynamical systems (differential algebraic equations of Index 3) with pulsed disturbances. To describe their discrete dynamics, a constrained variational integrator [1] is used. Using a discrete version of the Lagrange-d'Alembert principle yields a forced constrained discrete Euler-Lagrange equation in a position-momentum form that depends on the current and future time steps [2]. The desired optimal trajectory ( q opt , p opt ) and according control input u opt is determined solving the discrete mechanics and optimal control (DMOC) algorithm [3] based on the variational integrator. Then, during time stepping of the perturbed system, the discrete Riccati equation yields the optimal deviation control input u R . Adding u opt and u R to the discrete Euler-Lagrange equation causes a structure preserving trajectory as both DMOC and Riccati equations are based on the same variational integrator. Furthermore, coordinate transformations are implemented (minimal, redundant and nullspace) enabling the choice of different coordinates in the feedback loop and in the optimal control problem. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The Elastic Multi-Body Simulation (EMBS) is the state-of-the-art method when dealing with elastic deformations of components in complex mechanical systems. But the required FE-model representing the elastic structure contains several uncertainties concerning geometry, local and directional stiffness as well as damping phenomena. A mandatory Model Order Reduction (MOR) embodies further approximation errors. Due to the drawbacks of the conventional procedure, a novel approach is suggested, where the data of the elastic body model is directly gained from the results of an Experimental Modal Analysis (EMA). Therefore, the measured data is transferred to the Standard Input Data (SID) format by means of the software MORPACK (Model Order Reduction PACKage). The novel approach yields several challenges for which adequate solutions are presented. The feasibility is demonstrated at the example of an U-section. The accuracy in the higher frequency range can be increased, which is especially important for vibro-acoustic simulations. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper attends to a co-simulation approach for solver coupling in time domain. A general multibody system is divided into several subsystems, which are coupled by algebraic constraints. The coupling technique analyzed here is a linear-implicit predictor/corrector approach, i.e. coupling variables for the corrector step are calculated by one step of a Newton-iteration. Within the presented approach, the coupling conditions together with its first and second derivatives are enforced simultaneously at the communication-time points. This index-1 approach uses cubic polynomials to approximate the coupling variables. The space of polynomials of degree ≤ 3 is a four-dimensional vector space. One of the four degrees of freedom is used for a continuous approximation of the coupling variables at the communication-time points. The three remaining degrees of freedom are used in order to enforce the coupling conditions on position, velocity, and acceleration level. Due to the higher order approximation, the numerical errors are very small and a good convergence behavior is achieved. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An important trend in Computational Fluid Dynamics is towards high-order methods, as they offer a substantially lower discretization error for the same number of degrees of freedom (DOF). Examples are the Spectral-Element Methods (SEM) and Discontinuous Galerkin (DG) methods. Unfortunately, with most implementations the work load of such solvers increases drastically with the number of DOF, for example, when increasing the polynomial degree of the approximation. This issue gets particular pressing for elliptic solvers which are a vital building block in the time-stepping of the incompressible Navier-Stokes equations, resulting from pressure projection methods or implicit treatment of viscous terms. So far, this drastic increase of resources has hampered the use of SEM for higher polynomial degrees, such as 16 or more. The present contribution is located at this particular “Frontier of CFD” and proposes an SEM with linear scaling in the number of degrees of freedom. It is achieved independent of the polynomial degree, independent of the aspect ratio of elements, and involves constant iteration count when increasing the number of elements. The method is based on combining static condensation with block-Jacobi preconditioning and iterative substructuring. The latter two lead to a constant iteration count, while the former warrants linear operator complexity. In the presentation, the scheme is described in detail and applied to the construction of a Helmholtz solver. This solver is extremely fast and able to solve the Helmholtz equation with 10 10 unknowns on 240 cores in acceptable time. It thus enables competitive high-order SEM simulations even on small clusters and in this way expands the frontier of CFD towards highly accurate results requiring comparatively modest resources. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A novel variational framework for an interface zone model is developed and extended to poroelasticity. As was previously promoted in [1,2], the total energy of the system is composed by the bulk potential and fracture surface energy. In contrast to the phase-field method, the fracture surface is approximated directly along the edges of the finite elements in terms of interface zero-thickness finite elements. By introducing a new degree of freedom c (damage field) on the interface level, the solution is found by the minimization of the total potential energy with respect to the displacements and the damage field. An elastic interface constitutive law allowing for a normal and tangential displacement opening is adopted in the pre-fracture regime. Assuming, that a crack propagates according to the Griffith's criterion of brittle fracture, fracture initiates and propagates in normal opening mode. Biot's theory is applied both to the bulk and interface elements for the simulation of fluid driven fracture in fully saturated materials. The pressure field within the interfaces is averaged between the pressure at the bulk element faces. Pressure continuity is enforced by means of a penalty functional. The flow within the fracture is modeled by the cubic law taking the displacement and damage variables into account. A number of numerical benchmark tests, which include comparisons with experimental results and analytical solutions, are performed to demonstrate the performance of the model. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In multi-body systems, friction often occurs as a result of the contact between two bodies. The resulting forces may be desirable or undesirable, depending on the intended function of a technical system. Although a number of different causes of these forces have been worked out, the scientific understanding required for a systematic adjustment of friction towards satisfying given requirements is still incomplete. This makes it difficult for the designer to design an optimal friction contact. This is reflected in a large number of scientific publications in the associated fields. In order to cope with these challenges, a new, holistic approach is required to recognize and describe the general design principles of friction contacts. Based on the understanding of these principles, design guidelines in a design catalog can be formulated to support designers. In further steps, the designer can parametrize the frictional contact based on a catalog of diverse possible solutions. In the future, this tool should help the designer to find a simple, fast, and effective solution. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Aerodynamic simulation has reached a level of sufficient maturity, that not only benchmark problems are solved easily, but real application data can be delivered even for such complex configurations like rotorcraft. Leaving behind generic cases like driven cavity or isotropic turbulence and moving on to actual engineering, several fields more or less remotely related to aerodynamics have to be taken into account to provide accurate and reliable value. This is less a matter of ingenious invention, but much more so a careful selection of usable procedures for problems identified to matter, and mostly hard work, putting the pieces together and shaking all the wrinkles out. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Cable robots are widely applicable for various industrial tasks, where accurate trajectory tracking of the end-effector is an essential control objective. This is especially challenging for underactuated cable robots since they possess less actuators than degrees of freedom. Trajectory tracking can be achieved by using an inverse model based on servo-constraints. It is possible to solve the DAE problem in real-time, which makes an implementation on experimental setups straightforward. Stabilization of the tracking error can be achieved by a feedback controller which augments the feedforward loop in a two degree of freedom control structure. Effectiveness of the described method is shown in experiments on a cable robot test bench. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Time-optimal path following, i.e. moving a robot's end-effector optimally along a specified geometric path, is a very important and well discussed problem in robotics. Nevertheless, most of the existing approaches concerning this topic neglect the speed dependency of torque constraints. The present paper presents a method for taking such constraints into account within a dynamic programming approach. To this end, the problem is treated in parameter space. This allows for an optimal use of existing resources. Due to the demanding constraints, precise mathematical models of the robots are indispensable. A satisfying match between model and real system can usually be achieved by parameter identification. For this purpose, it is a common way to derive the equations of motion using nominal parameters (masses, position of center of gravity, inertia and friction parameters), rewrite the equations in terms of linearly independent base parameters, and determine them with the help of measurements. Nevertheless, a parametrization of the motor torques has to be introduced in order to be able to consider their constraints within the optimization. In contrast to this, we present a general toolchain, based on the Projection Equation that directly derives the base parameter representation and furthermore the coefficients of the parametrized equations of motion. A verification in terms of a numerical example for a six-axis industrial robot demonstrate why speed dependent torque constraints are preferable over constant torque constraints for time-optimal robot trajectories. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper discusses some dynamical aspects of a self-balancing Inertia Wheel Cube (IWC). The acceleration and deceleration of actuated flywheels is used to stabilize the IWC when balancing on one of its corners, which is an unstable equilibrium position. The orientation as well as the rotational velocity of the device are measured by an inertial measurement unit (IMU). The equations of motions are derived with the Projection Equation. Using the rotational velocity of the IWC as part of the generalized velocities leads to well-structured and interpretable dynamical equations. These equations are the basis for simulation, parameter identification, control synthesis, and stability analysis. The stability of the unstable equilibrium is investigated by means of the linearized motion equations. It can be shown that there are always uncontrollable states by invoking the conservation of momentum. Simulations as well as experimental results are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Contact mechanics is a branch of solid mechanics where two or more bodies are involved. The contacting points are characterized by a common tangential plane and a common normal vector given by the surface curvature of the bodies. Additional parameters of contact problems are the material of the bodies, the forces and torques acting on the bodies as well as their time history, location of the centers of mass and the roughness of the surface around the contact point. The classical contact problem is based on spherical bodies surfaces, linear-elastic material, constant static loading in normal direction and smooth surfaces. The rigorous solution [1] is often used for benchmarking. More details can be found in the monographs [2, 3]. The bodies of mechanical systems in engineering applications get in contact to each other mainly by impacts, rolling or sliding, or by joints. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, we show that a Stewart-Gough platform with ball screw linear actuators that do not inhibit a rotation between the upper and the lower cylinder, so-called unguided linear actuators, still has six degrees of freedom if universal joints are used as lower and upper joints. Such parallel mechanisms can be described as 6-UHPU types. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Model order reduction is widely used in the simulation of elastic bodies. In substructured settings, model order reduction using moment matching methods has shown to be advantageous. Using these methods, the minimal order of the reduced system depends directly on the number of interactions. This motivates the use of interface reduction methods. In this contribution an approach for interface reduction using a general singular value decomposition (GSVD) is presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Due to their low weight robots with flexible links are ideal candidates for use in dynamically demanding applications. Since the main goal of the robot control is to achieve precise positioning, the damping of oscillations due to low stiffness is imperative. Furthermore classical PD motor position control is insufficient for vibration damping. This paper presents an approach using an eye-in-hand camera for vibration damping of an elastic articulated robot with three actuated joints. The idea is to use the position of feature points in the camera image for generating a feedback signal. The image feature position is transformed into the joint space using the image Jacobian. The PD motor control is augmented by a proportional term w.r.t. a virtual arm angle. Experimental results of a comparison with a control concept based on acceleration sensors are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents a method for the identification of inertia parameters of non-holonomic omnidirectional (NHO) vehicles. NHO vehicles use several centered steerable standard wheels for their movement. They are omnidirectional in the sense that they are able to drive in each direction but may have to steer the wheels before starting the motion. A precise knowledge of the inertia parameters of such vehicles is e.g. mandatory for the application of model-based control approaches. The presented identification approach enhances a classic strategy consisting of the following steps: formulate the motion equations linear w.r.t. inertia parameters, determine uniquely identifiable (base) parameters, and plan an optimal excitation trajectory for the experiment, that is applicable to mobile robotic systems with non-holonomic (NH) constraints and locomotion limits. The overall approach is validated by experiments and yields promising results. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In rigid body mechanics, a body's configuration consisting of orientation and position have to be described, as well as angular velocity and velocity. There are several different ways to do this, leading to different configuration spaces. Popular choices include SO(3) × ℝ 3 , SE(3) or unit dual quaternions. All these configuration spaces possess a Lie group structure. We present the novel approach 𝕊 ⋉ ℝ 3 , which is a configuration space similar to SE(3), but describes the orientation in terms of unit quaternions instead of rotation matrices. Furthermore we show its relation to and advantages over other configuration spaces. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The considered systems contain dynamics on different time scales caused by different types and stiffnesses in potentials. For the slow motion, a coarse approximation suffices, but to resolve the fast motion, high accuracy is required. To avoid unnecessarily high computational costs, the idea here is to use polynomials of different degrees to approximate the slow and fast dynamics and quadrature formulas of different orders to approximate the different action terms. The approach is extended to holonomically constrained systems, where the Lagrange multiplier theorem is used to introduce constraint forces constraining the motion to the constraint manifold. The computational efficiency of the integrators is shown by means of two examples. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A non-smooth point mass model which mimics the locomotion of an earthworm is presented. The planar model consists of a chain with five elements on a rough ground. The distance between each pair of neighbouring elements is restricted by unilateral constraints. The contacts between the elements and the ground are subjected to anisotropic Coulomb friction. First, the equations of motion governing the impact-free motion are derived. Then, the impact equations are formulated which, together with the generalized Newton's impact law, describe the dynamics at instantaneous impacts. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A lumbar spine model with a PDSD was created using CT data and validated with experimental results of the same specimen. The material parameters of the spine and the stabilisation device were taken from literature and calibrated using experimental data. A fatigue model accounting for notch effect and cyclic plastic deformation was used to predict the fatigue life of the device regarding high-cycle loading and material softening of PEEK. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Blood flow simulation of complex arterial networks in three-dimensions generally involves assigning multiple inlets and outlets. This work investigates different kinds of boundary condition assigned on inlets and outlets in the Circle of Willis. These boundary conditions will be adopted in a way that a realistic velocity profile and pressure in the main brain arteries are achieved. The result of this work will be used for Fluid–structure interaction simulations. As the force applied on the artery wall depends on the blood pressure, the goal is to achieve a pressure boundary condition based on the in-vivo flow rates in each artery. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper describes non-classical locomotion based on the variation of the contact force. The motion of a locomotion system on an inclined plane is considered. The contact force between the locomotion system and the inclined plane can be influenced by the motion of internal masses. Therefore a mechanical model with two internal masses is introduced. The friction between the locomotion system and the environment is described by COULOMB's law. The motion of this locomotion system is investigated and analyzed by using the averaging method of BOGOLJUBOV and MITROPOLSKI. Furthermore the influence of different parameters on the locomotion characteristics like the direction of movement, the stationary velocity and the maximum inclination angle is shown. A prototype based on this locomotion principle is built up for experimental investigations. Additionally, simulations are used to analyze the locomotion system. The experimental values are compared to the theoretically results and confirm the variation of the contact force as an option to enable a controlled locomotion. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Aortic aneurysms are a common disease among older patients. Aneurysm ruptures cause more than 150 000 deaths annually [2]. One of the main risk factors which lead to the abnormal enlargements of vessels (〉150% of original size) is arterial hypertension. This contribution presents a modeling approach, where the cyclic loading of the artery caused by the blood pressure leads to fatigue inside the arterial wall. The arterial wall is considered as a composite material, where a matrix (ground substance) is reinforced by collagen fibers consisting of fibrils connected by proteoglycan (PG) bridges. These PG bridges support interfibrillar sliding leading to lower fibril stretch [6]. Molecular adhesive bonds rupture under any pulling force if the force is held sufficiently long enough [1]. This rupturing over time leads to a decrease in the density of PG bridges, higher stretches in the fibrils, more damage inside the fibrils and finally to fatigue of the soft tissue which causes the abnormal enlargement. Finally the model is compared against experimental data of uniaxial tension tests and used in a FEM simulation to study the emergence of aortic aneurysms under arterial hypertension. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Skeletal muscle tissue shows a wide variation in its mechanical response for different persons or different muscle types of one single person. These distinct mechanical properties are due to variations in the microstructure of the material. For skeletal muscles, especially the arrangement and the stiffness of collagen fibres in the connective tissue define the macroscopic passive stiffness, while the sarcomeres (contractile units) enable an active contractility of the muscles. Phenomenological models lack the ability to take into account such microstructural variations in a natural way and need to be fitted to experimental data, which is, however, not available for every desired muscle type. Thus, this work presents a homogenisation-based multiscale model for skeletal muscle tissue which enables to include microstructural properties in a continuum-mechanical framework. The underlying homogenisation is done by means of the tangent-second-order (TSO) method, which is appropriately extended in order to account for the transversely isotropic behaviour of the muscle material. Moreover, an angular-integration model is embedded for a comprehensive description of the connective tissue. Concluding, the presented model allows to directly include microstructural-based material properties on the continuum-mechanical macroscale and yet avoids the expensiveness of computational homogenisation methods, like FE 2 , by using well-founded analytical homogenisation techniques. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The human liver is the most important organ according to metabolism processes in the human body and responsible for the detoxification of medications and toxins. During detoxification processes the harmful components are transported via the blood perfusion and metabolised in the liver cells. Toxic amounts of drugs can harm the liver and affect the important liver functions. The critical dose of medications varies due to different individual preconditions of the human body. Additionally the detoxification can be affected by several liver diseases for example a non-alcoholic fatty liver disease (NAFLD). To analyse the depletion of medicines and the interaction between the detoxification and NAFLD, we use a multi-scale and multi-phase model to calculate the hepatotoxicity in the human liver using the example of the pain killer paracetamol. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution, results regarding fluid-structure interaction (FSI) simulations for three-dimensional arterial walls are presented. In detail, a benchmark problem for FSI simulations in arteries of sufficient complexity, which combines sophisticated nonlinear models for the fluid and the structure, cf. [1], as well as a short segment from a patient-specific arterial geometry are considered. For the patient-specific arterial geometry a specific inflow profile suited for realistic geometries and simplified boundary conditions for the outflow are taken into account. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The ageing society leads to an increased risk of femoral neck fractures. Besides endoprotheses and established head-conserving implants, the rotation-stable screw anchor is used for surgical treatment. In this in vitro study, the influence of cemented versus non-cemented implants is tested. Therefore, a novel test set-up is used that is capable of simulating the load during gait cycles. Thereby, the transferability to clinical practise shall be increased. Additionally, time-series data is recorded to evaluate clinically relevant parameters during the applied cyclical load. The results show that the test set-up enables deeper insight to the implants behaviour during loading, which is of relevance due to the differences that can be observed between the cemented and non-cemented implant. Additionally, the results are compared to the literature. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A new therapeutic approach in the treatment of small focal articular defects is the implantation of an acellular collagen-based scaffold. Replacement materials need to fulfil high requirements in terms of biocompatility and mechanical properties. Ideally, they feature similar mechanical properties as native articular cartilage. The aim of this study is to experimentally and numerically analyse a clinically available implant. Therefore, we perform unconfined compression tests and use a phenomenological material model to identify material parameters of the viscoelastic material. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The human thumb possesses joint axes with intricate descriptions, which enable the thumb to perform complex motions like opposition. To validate a thumb multibody model kinematically, we firstly study the difference in the volumes of the thumb tip workspace for the maximum range of motion (RoM) and the grasp RoM. We compare the volume difference for five models (with same joint designs but different axes locations and orientations) with data from literature. Secondly, we compute the rotation of the thumb along the longitudinal axis (internal rotation) for one joint for different postures. We compare the rotations for the five models with measured data from literature. In both checks, the results obtained from simulation are in close agreement with literature data and consequently the thumb model's kinematics is validated. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The modelling of biological processes like the metastasation of lung cancer in brain tissue requires the inclusion of the major processes at the metastasis site as well as to identify model parameters from experiments. In this regard, experimental data from proliferation, malnutrition and drug experiments are embedded into a continuum-mechanical metastases model. Successfully implemented, such models can serve as prototype tools to estimate the metastases growth and response to therapeutic applications. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Pulling actuators play an important role in biomechanical simulations. In most animals, muscles are the actuators exerting torques onto the joints. These torques highly depend on the muscle line of action or, in other words, muscle lever arms. Common methods focus either on single-joint movements, on two-dimensional problems, or on imitating physiological lever arms only in a small working range. However, especially in complex multibody simulations, where reduced descriptions of muscles as massless, visco-elastic, active bands are used, a correct representation of lever arms is mandatory for a large range of joint angles for all degrees of freedom. To address these issues, we developed a new design and computational algorithm for modeling the path of linear pulling actuators. The method is based on finding the shortest muscle path while the actuator is lead through a small number of two-dimensional shapes. It allows for multiple degree of freedom and high-amplitude movements as well as combinations of both, ensuring reasonable lever arms at all possible joint configurations even for muscles spanning more than one joint. We applied this method to a multibody model of the human musculoskeletal system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The objective of the presented paper is to compare the usage of different digitization methods to generate finite element models of dental structures and restorations. Four different virtual models were generated by using intraoral-, CBCT-, CT- and micro-CT datasets. Subsequently there were compared due to their field of view (FOV), accuracy and radiation exposure for the patients. Depending on the specific application all four virtual models showed a qualitative and quantitative correlation associated with in-vitro and in-vivo studies. Further the influence of artifacts and application limits were classified with weight functions for the use in a database. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: It is supposed that the vision of an integrated Overall Human Model (OHM) can be realised by the combination of isolated models. By this means, a so-called OHM-toolbox contains these models, which need to be extended and/or linked to each other depending on the chosen application. However, this implies the need to bridge over several length and time scales as well as to combine different physical effects and numerical approaches. In this regard, the proposed contribution is related to the description of one part of this toolbox, namely, the overall mechanical behaviour of human brain tissue. As an application-driven organ model, it can substantially contribute to a holistic understanding of various complex processes, such as the study of brain-tumour treatment. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the European Union, fatty degeneration of the liver is a major problem in human health care. Approximately 20% to 30% of individuals in Western countries have a non-alcoholic fatty liver disease (NAFLD). The high number of people concerned can be explained by the high sensitivity of the liver due to negative environmental influences as addiction to high fat diets or alcohol consumption. High fat diets are the leading cause for NAFLD (steatosis), which is characterized by an accumulation of lipid droplets in the liver tissue. The growing fat has a high impact on the perfusion of the blood through the liver. The anatomy of the organ is characterized by a complex vascular system which changes on the different scales from a vascular branching tree to micro vessels, called sinusoids, in liver lobules. To capture the interplay between fat deposition arising in the microstructure and the perfusion on the organ scale it is important to couple the processes on each scale. For this we present a computational model for the human liver which is composed of three coupled sub models for the organ, lobule and cell scale. Due to the complexity of the organ we apply a multi-component/tri-phasic/tri-scale approach, which is founded on the publication of Ricken et al. [2], coupling all relevant aspects to visualize the coupling between the fat metabolism and the hepatic perfusion. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The human inner ear or cochlea is a bone structure of spiral shape and is composed of mainly two conical chambers which are filled with fluid and separated by a soft membrane, referred to as the basilar membrane. At the apical end, both chambers are connected through a small opening, the helicotrema. At the base, the chambers are closed by the stapes footplate and the round window membrane. In case of a normal ear, sound is received by the eardrum, transmitted through the middle ear ossicles and finally excites the inner ear fluid through the vibration of the stapes footplate. According to present hearing theory, this leads to pressure waves in the cochlear fluid which in turn results in characteristic vibration behavior of the basilar membrane. Related to the sound frequency, hair cells in certain areas of the basilar membrane are stimulated and cause hearing nerve stimulation. In order to predict the effect of inner ear diseases on hearing impression as well as to develop new hearing implants, a deeper understanding of the cochlear dynamics is needed. However, since the cochlea represents a closed hydraulic system with a complex geometry, the motion of the basilar membrane as well as the fluid pressure can hardly be measured. Therefore, a numerical model of the uncoiled cochlea is developed representing the fundamental physical effects occurring in the cochlea. Taking the fluid-structure interactions into account, the transfer behavior of the cochlear system is investigated for different excitation frequencies within the auditory frequency range of humans. The simulations show the passive vibration of the basilar membrane resulting in the characteristic traveling wave. These results allow to study the mapping of the excitation frequency to its characteristic pattern along the basilar membrane, called tonotopy. Further, the spatial fluid pressure distribution along the cochlear chambers is evaluated and allows new insights into the cochlear physics. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution focuses on the use of a new method to reduce the computational demands of fatigue damage computations using continuum damage mechanics. The LArge Time INcrement (LATIN) method incorporates a model order reduction approach namely the proper generalised decomposition (PGD). LATIN has been extended to tackle damage problems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This study is concerned with theoretical and numerical aspects of a thermodynamically consistent gradient-extended damage-plasticity model which is based on a ‘two-surface’ approach: damage and plasticity are treated as, in principle, independent physical mechanisms by using separate yield and damage criteria as well as individual sets of loading / unloading conditions. Such a model is especially appealing from a practical point of view since it can naturally account for various situations in which the model's behavior is either (quasi-)brittle-like, ductile-like or possibly anything in between. The model's algorithmic treatment at the local integration point level requires special considerations. In this regard, two inherently different strategies are implemented and tested during the study and are briefly discussed here. A numerical benchmark test reveals that the proposed gradient-extended damage-plasticity model is well suited for counteracting the results' mesh size dependence in finite element simulations involving damage. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Classical molecular dynamics (MD) simulations are performed to study the stress-strain behaviour of armorphous silica glass (a-SiO 2 ) at small time and length scales. Various amorphous states are generated by quenching molten SiO 2 using a two-body and a three-body interaction potential. This quenching process is carried out for different cooling rates. The structural properties of a-SiO 2 are validated through a comparison with other numerical and experimental results. Finally, tensile tests are performed on a-SiO 2 until fracture occurs, and the cooling rate influence on the tensile strength is analysed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A 3-D finite element modelling (FEM) approach of the human aortic valve (AV) is developed to study its extra-cellular matrix (ECM) destructive remodelling caused presumably by ventricular diseases, assuming that the function, deformation and performance of the valve is strongly dependent on its geometry. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In an aging society where the number of joint replacements rises, it is important to also increase the longevity of implants. In particular hip implants have a lifetime of at most 15 years. This derives primarily from pain due to implant migration, wear, inflammation, and dislocation, which is affected by the positioning of the implant during the surgery. Current joint replacement practice uses 2D software tools and relies on the experience of surgeons. Especially the 2D tools fail to take the patients' natural range of motion as well as stress distribution in the 3D joint induced by different daily motions into account. Optimizing the hip joint implant position for all possible parametrized motions under the constraint of a contact problem is prohibitively expensive as there are too many motions and every position change demands a recalculation of the contact problem. For the reduction of the computational effort, we use adaptive refinement on the parameter domain coupled with the interpolation method of Kriging. A coarse initial grid is to be locally refined using goal-oriented error estimation, reducing locally high variances. This approach will be combined with multi-grid optimization such that numerical errors are reduced. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A combined continuous-discontinuous approach to fracture is presented to model crack propagation in 3D. The damage evolution governs the discrete crack advancement and the direction of the crack propagation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this project, the punching process of carbon fiber reinforced plastics (CFRP) is investigated numerically and experimentally. Punching presents a low cost and potentially high quality manufacturing technology for piercing, but has not been investigated sufficiently so far for CFRP. The project aims on the key mechanical processes from a damaging point of view. The goal of the project is to identify the principle influence parameters on the quality of the cutting face from a simulational and an experimental point of view. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The implementation of a path-following method for the simulation of quasi-brittle failure is discussed, which employs a constraint function based on the overall dissipation increment associated with the softening material. Spurious mesh-dependency is avoided by a nonlocal integral formulation of the isotropic damage model. The performance of the method is illustrated for a one-dimensional bar problem in which snap-back behavior is observed immediately after damage initiation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution, an experimental study and FE simulations based on J-integral theory and the phase-field modelling approaches are presented in order to systematically study the temperature and strain-rate dependency of glass fracture behaviour. First, a series of three-point bending tests are successfully carried out under different stain-rates and temperatures. Secondly, numerical modelling of the bending tests with the introduction of a micro crack yields the stress-strain response, which serves to the calculation of J-integral values, in order to describe the glass fracture resistance in terms of energy. At the end, the critical energy release rate serves as a bridge connecting the J-integral theory with the phase-field modelling, where a dynamic fracture model with crack propagation is realised as a new direction for further researches. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)