ALBERT

Description: The theory of invariant continuum mechanics is based on the concept that forces and stresses are defined as elements of the cotangent bundle of the configuration manifold. While body and physical space are modeled as differentiable manifolds, the infinite dimensional configuration manifold is given by all configurations of the body in the physical space. In this paper a virtual work principle is postulated which leads together with an induced traction stress and Stokes' theorem directly to the local equilibrium equations and the traction boundary conditions. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We discuss numerical results of nanodomain interfaces using a new extended molecular statics algorithm for ferroelectric materials. The new algorithm is able to not only calculate the change of the polarization behavior caused by strain but also the influence on the polarization behavior due to mechanical stress. The size effects of 180° head to head and tail to tail nanodomains have already been investigated. This study also considers 90° domain walls and discusses the impact of mechanical stress on polarization patterns and system energies of nanodomain interfaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Volume 16 (2016) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the Joint 87 th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, held 7 – 11 March 2016 at TU Braunschweig, Germany. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections Minisymposia M 1 Computer algebra M 2 Immersed boundary methods M 3 Linear and multilinear methods for electronic structure calculations M 4 Mechanics and model based control M 5 Space-time methods for parabolic and hyperbolic PDEs M 6 Robust simulation of mechanical systems with uncertainties M 7 Control of partial differential equations Sections 1–29 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 Applied stochastics 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 24 History of fluid mechanics and history, teaching and popularization of mathematics 25 Algebra, logic and set theory 26 Discrete mathematics and theoretical computer science 29 Mathematics in the sciences and technology Young Researchers' Minisymposia YR 1 Multiscale evolutionary problems YR 2 Mechano-regulated growth and remodeling in biological tissues YR 3 Dedicated regularization for variational image processing YR 4 Variational integrators in simulation and control YR 5 Impinging jets Zentralblatt Meeting zbMATH Mathematical research data management

Description: The drive belt set on two pulleys is considered as a plane elastic rod. The nonlinear theory of rods with tension is used. The static frictionless contact problem for the rod is formulated. The derived boundary value problem for the nonlinear ordinary differential equations is solved by the finite difference method and by the shooting method by means of computer mathematics. The belt shape and the stresses are determined. The contact reaction and the contact area are obtained in the solution. A benchmark study of extensible and inextensible models is performed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In many fields of engineering the acoustic behavior has to be determined, e.g. the sound distribution in a room or the sound radiation into the surrounding. Often, the goal is to obtain a sound pressure field such that disturbing noise is reduced to an acceptable level. In room acoustics, sound absorbing materials are often used to obtain this goal. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative. Here, an indirect formulation, which uses the single layer potential, is used as basic boundary integral equation. The convolution quadrature method is applied for time discretisation, which allows a simple formulation of the Robin boundary condition in the Laplace domain. Convergence studies with a refinement in space and time show the expected rates. A realistic example for indoor acoustics, the computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics. The absorbing boundary condition shows the expected behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution gives a short introduction into the topic of fluid-structure-control interaction (FSCI). This is a multi-field problem, where three fields are coupled, namely a fluid-flow, structural dynamics and closed-loop control of structures. The interactions are identified as surface-coupling of fluid flow and structural dynamics as well as signal-coupling of structural dynamics and closed-loop control. At first a simple model problem is introduced, which allows an efficient investigation of the convergence behavior and stability of such kind of problem. In this context an iterative partitioned approach, using a serial Gauß-Seidel scheme, is presented. Finally, the insights gained by the model problem are used to set up a multi-dimensional numerical experiment. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The output regulation problem is solved for an ODE plant driven by a parabolic actuator with spatially varying coefficients. Applying the backstepping transformation to the actuator allows the solution of the regulator equations in closed-form and thus the formulation of the solvability condition. An output feedback regulator is obtained by designing a disturbance observer using delayed measurement and a reference observer that both achieve finite-time convergence. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The identification of parameters in systems described by one-dimensional linear partial differential equations with constant coefficients is addressed. The algebraic approach used for identification has previously been applied to different infinite dimensional systems. Here, an algebraic algorithm is presented generalizing the underlying ideas from these examples to the class of systems mentioned before. It derives simple polynomial equations relating the concentrated measurements and the unknown parameters by using the Laplace transform and applying methods of commutative and differential algebra such as the Ritt algorithm. In the end, the identification of parameters requires only the calculation of convolution products of measurement signals. A vibrating string serves to illustrate the theory. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Among the most challenging problems in present day mechanics is the realistic simulation of the human kinetic behavior which requires correct modeling of the muscles – the human actuators. We are, therefore, implementing and validating a 1-D massless Hill-type muscle model in the program Neweul-M 2 . As a part of this effort, various anatomical and physiological parameters need to be chosen prior to the simulation. These parameters are always subject to natural variability or scatter. Therefore, it is important to consider those parameters as uncertain fuzzy parameters and then determine the sensitivity measures of the parameters involved in various simulation scenarios using the program Famous. The applied sensitivity analysis quantifies the influence of individual parameters or subsets of parameters on the output quantity of interest. Thus, this analysis identifies those parameters with large influence on the simulation response of muscles which, therefore, needs to be chosen very carefully. (© 2016 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 want to use it to control constrained dynamical systems (differential algebraic equations of Index 3). To describe their discrete dynamics, a constrained variational integrators [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. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The performance of a model-based tracking controller depends on the quality of the underlying model. Especially for flexible multibody systems, the derivation of a suitable model and the subsequent controller design are challenging tasks. In the paper, it is shown how in a straightforward approach a feed-forward controller for a flexible multibody system is designed based on a simplified model which approximates an elastic beam by a combination of rigid beams and force elements. Furthermore, the modelling error due to this harsh simplification is included as uncertainty in the simplified model and considered in the model-based feed-forward controller design using fuzzy arithmetic. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A new index reduction approach is developed to solve the servo constraint problems [2] in the inverse dynamics simulation of underactuated mechanical systems. The servo constraint problem of underactuated systems is governed by differential algebraic equations (DAEs) with high index. The underlying equations of motion contain both holonomic constraints and servo constraints in which desired outputs (specified in time) are described in terms of state variables. The realization of servo constraints with the use of control forces can range from orthogonal to tangential [3]. Since the (differentiation) index of the DAEs is often higher than three for underactuated systems, in which the number of degrees of freedom is greater than the control outputs/inputs, we propose a new index reduction method [1] which makes possible the stable numerical integration of the DAEs. We apply the proposed method to differentially flat systems, such as cranes [1,4,5], and non-flat underactuated systems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The main objective of the present work is the development of a simplified, efficient and easy-to-implement single-phase material model, which is able to describe the essential effects characterising the behaviour of multi-phase saturated materials, such as of intervertebral discs (IVDs). The presented new model mainly focuses on extending a viscoelastic material model in order to not only take the mechanical behaviour of the solid part into account, but also the fluid-flow-dependent behaviour of the material. By applying this model, the complexity and constitutive parameters are reduced, the implementation is more convenient and the experimental investigations can be better supported in comparison to multi-phase material models of IVDs. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Identification of unique material parameters for the media and adventitia in the case of arteries involves many challenges. Tension-inflation experiments were performed on the internal mammary artery and the axial force and the radial displacements were used to identify the material parameters. It will be shown that these experimental data are not sufficient to uniquely identify the material parameters of the passive response in human arteries. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the effect of different stress states on damage and failure behavior of ductile materials. To be able to model these effects a continuum damage model has been proposed taking into account the dependence of the stress intensity, the stress triaxiality and the Lode parameter on the constitutive equations. The model is based on the introduction of damaged and fictitious undamaged configurations. Only experiments are not adequate enough to determine all constitutive parameters. Therefore, additional three-dimensional micro-mechanical simulations of representative volume elements have been performed to get more insight in the complex damage mechanisms. These simulations cover a wide range of different void sizes, void shapes and void distributions. After all, the results from the micro-mechanical simulations are used to propose the damage equations and to identify corresponding parameters. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An approach to model the deterioration of steel structures is presented by transferring the results of a continuum damage mechanics analysis to an extended beam model which can account for the loss of structural integrity. Damage starts at the microscopic level by the initiation, growth and coalescence of voids with decreasing material resistance followed by the formation of microcracks at the mesoscale. Nevertheless, the material behavior can be sufficiently modelled on a phenomenological basis taking into account viscoplasticity, hardening effects and damage evolution. The associated model parameters are identified with the help of an evolutionary algorithm adapting numerical to experimental results. Using the finite element method a nonlocal formulation of the damage variable is required to obtain mesh-independent results by structural analysis. The maximum element size is limited by the small magnitude of the internal length. Therefore, numerical analyses of large scale 3D steel structures are computationally expensive. To reduce the effort a beam element is proposed to account for the plastic hinges and the loss of resistance in the course of damage evolution. The corresponding relationship of bending moment and curvature bases on the continuum damage mechanics model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Printed conductive paths can transmit electrical information and form an alternative to conventional wiring. In lightweight applications, where the reduction of weight is crucial, printed conductive paths and electronics could help to diminish the total mass of the structure. A possible application in aeronautics is Structural Health Monitoring (SHM) - a collective term describing the structural integration of electronics that serve as a central nervous system to detect damages. As the electronics cannot only be printed on surfaces but also in between the layers of CFRP materials, it is currently under investigation whether the electronics favor delamination. To describe the electronics-CFRP interface failure numerically, a suitable approach for a finite element analysis shall be found. Based on a homogenized and simplified description of the interface, different numerical approaches are presented and advantages and disadvantages are considered. The most promising approach is discussed in greater detail and first numerical simulations are shown. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The aim of this work is to numerically simulate the gelation of a crosslinking polymer, which is a very complex process involving chemical reactions and phase transitions from a viscous fluid to a viscoelastic solid. A phenomenological model is proposed to simulate the gelation process of agarose droplets, considering the thermal boundary conditions. The numerical model is implemented using the finite element package FlexPDE. The temperature- and time-dependent degree of gelation and the deformation of the droplets during the gelation process are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush-Kuhn-Tucker (KKT) conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with gradient enhancement. An important emphasis of this research is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the KKT conditions in the multi-surface damage-plasticity setting. Response simulations for a representative inhomogeneous boundary value problem are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Damage accumulation and creep-fatigue interaction are investigated and depicted for a continuum damage model proposed for the lifetime prediction of bonded steel joints with the structural adhesive BETAMATE 1496V™. The nonlinearity of damage accumulation is caused by the nonlinearity of damage interaction as a result of the identified parameters. In consequence of the nonlinear accumulation, the model allows for the loading sequence effect, which is the influence of the chronological order of the load values on the lifetime. Although the nonlinearity of the damage accumulation is not very pronounced, the model prediction is in good agreement with lifetimes from tests with service loading of the adhesive at hand. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In lots of lightweight applications, constructions are also made by honeycomb sandwiches but little is known about failure and dynamic behavior of sandwich plate connections. In this research, an experimental and simulation study of the mechanical and failure behavior of honeycomb sandwich plates and joints are performed. In detail, series of tensile test have been conducted under quasi static conditions and failure behavior and resistance of the specimens are investigated. The specimens are made by phenolic resin-impregnated aramid paper as core and two different layers of glass fiber reinforced plastic as face sheets in each side. In addition to the experimental tests, numerical simulation with finite element models are performed in Abaqus. Failure modes are investigated and finally a good agreement between test data and simulation results is achieved. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Nowadays robotic manipulators are considered to perform a wide range of tasks. Since robotic systems consisting of multiple manipulators are capable of handling a variety of tasks that cannot be executed by single manipulators, cooperation of multiple manipulators is becoming increasingly interesting in particular for industrial applications. The interaction with other manipulators, respectively the environment, requires an extension of the conventional position control in order to achieve a desired compliance, and thus to limit the interaction wrench so to avoid damaging the involved objects. In this contribution the cooperation of two industrial manipulators, a Stäubli RX130L (6-DOF) and a Stäubli TX90L mounted on a linear axis (constituting a redundant 7-DOF manipulator), is addressed applying an impedance control scheme. The manipulation task is to grasp an object with both manipulators and to follow a prescribed trajectory by simultaneously limiting the contact forces between the manipulators and the object and ensuring a compliant behavior towards the environment. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Proteins of the FtsZ (filamentous temperature-sensitive Z) family establish complex polymeric spatial patterns in plastids of the moss Physcomitrella patens. These structures represent a "plastoskeleton" that might contribute to plastid shape and stability. The aim of this work is to develop computer models of FtsZ network connectivity and dynamics. These computer models are developed from green fluorescent protein (GFP) images obtained by Prof. Reski's Plant Biotechnology group at the University of Freiburg by means of laser scanning confocal microscopy. Subsequently, structural reconstruction techniques based on cellular automata algorithm are applied on the raw image data to compensate for any information that is lost in the process of imaging. Segmentation of the processed data will result in the computer model of the targeted structures, which are used for further analysis. Model generation and experimental testing in the moss system is conducted in an iterative process with the aim of both forward and reverse biomimetics. A developed image processing algorithm with the aim of quantification of structural characteristics is utilized to extract structural features of the FtsZ network in Physcomitrella enabling us a statistical analysis on the extracted data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, an approach to compute the passive rotation in a parallel hexapod structure is introduced which is based on quaternions. The advantage of this approach is that it prevents from unnecessary trigonometric or inverse trigonometric functions, which reduces rounding errors and saves memory. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For an efficient approximation of the local and global deformation behavior, impact simulations using reduced elastic models can be performed. Modally reduced models require a large number of eigenmodes to capture all local deformation effects. For this reason, the use of static shape functions in the contact area is recommended. However, due to high eigenfrequencies introduced by the static shape functions, the time integration is no longer efficient. Hence, this work presents an approach to reduce the influence of these high frequencies on the time integration. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Biped walking robots present a class of mechanical systems with many different challenges such as nonlinear multi-body dynamics, a large number of degrees of freedom and unilateral contacts. The latter impose constraints for physically feasible motions and in stabilization methods as the robot can only interact due to pressure forces with the environment. This limitation can cause the system to fall under unknown disturbances such as pushing or uneven terrain. In order to face such problems, an accurate and fast model of the robot to observe the current state and predict the state evolution into the future has to be used. This work presents a nonlinear prediction model with two passive degrees of freedom (dof), point masses and compliant unilateral contacts. We show that the model is applicable for real-time model predictive optimization of the robot's motion. Experiments on the biped robot LOLA [1] underline the effectiveness of the proposed model to increase the system's long term stability under large unknown disturbances. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The macroscopic mechanical response of skeletal muscle tissue is mainly influenced by the properties and arrangement of microstructural elements, such as, for example, sarcomeres and connective tissue. Like for many biological materials, the mechanical properties of skeletal muscle tissue can vary quite significantly between different specimens like, for example, different persons or muscle types. Current state-of-the-art continuum-mechanical muscle models often lack the ability to take into account such variations in a natural way. Further, phenomenological constitutive laws face the challenge that appropriate material parameter sets need to be found for each tissue variation. Thus, the present work aims to identify the microstructural features and parameters governing the overall mechanical response and to incorporate them into a macroscopic material model by applying suitable homogenisation methods. The motivation hereby is that the estimation of material parameters for microstructures, such as collagen fibres, can be done in a more reliable and general way and that fluctuations between specimens are included by, for example, adapting the alignment of the collagen fibres inside the muscle. Moreover, instead of computationally expensive homogenisation methods like FE 2 , this work proceeds from well-founded analytical homogenisation techniques in order to keep the model as simple as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A lumbar spine model without instrumentations was created using CT data and validated with experimental results of the same specimen. The specimen was loaded with pure moments in a spine test rig. The material parameters were taken from literature and adapted for better simulation of the experiments. The results show that further calibration of the material parameters and the implementation of additional ligamentous structures are necessary to simulate the spine's motion reliably. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A continuum-mechanical finite element model of skeletal muscle contractions that includes force enhancement based on actin-titin interaction is presented. This model can simulate muscles with a descending limb in the total force-length relation, which has previously led to unstable behaviour. The model predictions are in agreement with results of active stretch experiments. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In comparison to other eukaryotic cells, mammalian oocytes are characterised by a relative high diameter allowing in turn a straightforward micromechanical testing to study their mechanical properties. The structure of mammalian oocytes is characterised by the so-called zona pellucida (ZP), a thick glycoprotein layer, surrounding the cells interior, the ooplasm. In contrast to other cells, where the load is mainly carried by inner cell structures, in case of oocytes a huge amount of external loads is carried by the ZP. Aim of this work is the determination of the mechanical properties of oocytes. Therefore, a micromechanical setup has been developed and installed on a microscope. Beside the determination of the force-strain relation during loading, the deformation of the oocytes has been recorded optically, too. Both, the force-strain curves and the optical recordings build the basis for a proper parameter identification technique based on the inverse finite element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Temperatures below freezing point represent a common threat to standard construction materials, as a phase change of the pore content from liquid water to solid ice frequently leads to damage. However, frost-resistant plants are able to withstand many cycles of freezing and thawing without any damage. Hence, the objective is to identify and analyse structural factors of frost-resistant plant tissues and to develop a model, which includes their functional behaviour. Since frost-resistant plant tissues are formed by ordered arrangements of cells with prescribed shape and size, they can be understood as an (anisotropic) natural porous material. Therefore, a customised modelling strategy based on the Theory of Porous Media (TPM) is proposed, which allows for the description of structural traits and the formation of ice within plant tissues. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Actin plays a crucial role in the mechanical response of cells. Together with other proteins, it also drives protrusion, motility and cell division. Two important aspects of the mechanical modeling of this kind of protein are considered: its microscopic and macroscopic behavior. At the microscopic level, we start with a model proposed by Holzapfel and Ogden [1] providing a relationship between the stretch of a single polymer chain and the applied tension force. The model is advantageous as it simulates the so-called ‘exceptional normal stresses’. This effect is typical for biopolymers and contradicts with the Poynting effect typically observed in rubber-like polymers. The multiscale finite element method (FEM) is applied to simulate the effective mechanical behavior of cell cytoplasm. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This work investigates the combination of optical motion capturing data with optimal control simulations of human motion, which can be important in a wide range of applications in the professional as well as the private sector, ranging from health and ergonomics over human-machine-interaction to sports and games [1–3]. There are methodically very different approaches to include optical measurement data in the simulation of human motion, see e.g. [4–6]. Two different approaches to combine data and simulation are investigated in this work. Either we use a soft constraints approach, where the difference of simulated and measured marker positions is part of the objective function (1), or we formulate an hard constraints approach with nonlinear constraints that set an upper bound on this difference (2), while the objective function is purely physiologically motivated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The objective of this work is to develop a finite element model of active human skeletal muscle, which can mimic its contraction behaviour. The model is then used to analyse the effects of active muscle contraction into occupant kinematics and injuries during rear-end collision. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Wound healing in epidermis is a complex physiological process in which new cells are created to repair the damaged tissue. The timing of cell division and growth mechanisms in wound healing are influenced by biological, mechanical and medical factors. In this work we aim to provide a numerical model based on the observations realised in in-vitro experiments for the understanding of wound healing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Originated from a lung tumour, cancer cells can spread via the blood-vessel system, travel to the cerebrum and may pass the blood-brain barrier. The extravasation is followed by migration, and the formation of micrometastases. Further proliferation causes interveined metastases. A pressure-driven infusion of a therapeutic solution counteracts the disturbance by the metastases within the brain. These processes are described with a continuum-mechanical model based on the Theory of Porous Media. Numerical applications demonstrate the feasibility of the model and include multicellular-tumour spheroid experiments in the macroscopic simulation of metastases growth and atrophy. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In order to better understand and ease the determination of material and model parameters required for the macroscopic modelling of brittle fracture, a bottom-up comparative study between molecular dynamics (MD) simulations and the continuum phase-field modelling (PFM) is carried out. In particular, based on the MD simulations of fracture of a highly brittle material, a number of PFM parameters such as the width of the transition zone between the damaged and the undamaged material, the crack resistance and the elasticity modulus are estimated. This study opens the door for an efficient way for multi-scale modelling of fracture. To illustrate this approach, a comparative two-dimensional numerical initial-boundary-value problem (IBVP) for the highly brittle aragonite (CaCO 3 ) is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Hydraulic fracturing has led to controversial public debates about its risks due to environmental issues, such as increased seismic activity or drinking water contamination. The technique is primarily used to gain crude oil or natural gas from unconventional wells. To this end, a high pressurized fracking fluid is injected into a wellbore to fracture deep-rock formations, leading to growing cracks, a subsequent increase of permeability in these formations and thus to an increased flow of natural gas and crude oil. To weight the risks and the perspectives of hydraulic fracturing a profound understanding of the involved processes is crucial. Numerical simulations are the most cost efficient way for the required studies, but demand a reliable model with a stable implementation. We propose a canonical minimization principle for the Biot-type fluid transport in porous media based on only two constitutive functions, that is the free energy function , and a dissipation potential , [1]. This formulation is coupled to a phase-field approach for fracture which characterizes an intuitive and descriptive regularization of a crack surface that converges for vanishing length-scale parameter to a sharp crack. The crack phase-field allows for a distinct incorporation of an extra fluid flow within cracked regimes of the solid [2]. This extra fluid flow is modeled according to Poiseuille law for laminar flow, yielding an implementation via a change of the permeability tensor, i. e., making it a function of the crack opening width, formulated itself in terms of the strain and the gradient of the crack phase field. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Within the XFEM often near linear dependencies between the standard degrees of freedom and enriched degrees of freedom and also among enriched degrees of freedom occur. During the last years, several remedies to that problem have been presented. Here, an extension of the regularization technique described in [1] to finite deformation problems and inelastic material behaviour as well as to multifield problems is proposed. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Phase field modelling of brittle fracture is very well understood today. However, the attempts of investigation of elasto-plastic fracture by the phase field approach are limited. This contribution deals with the investigation of a phase field model for elasto-plastic fracture. Based on a free energy density comprising elastic, fracture and plastic contributions, the model describes an extension of the linear elastic model towards von Mises plasticity. In this work it is analyzed numerically to which extend analytical findings concerning the interpretation of the model parameters in 1D are transferable to 2D scenarios. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Dynamic fracturing is an active field of research in which some phenomena like crack branching are only partly understood. The origin for most theoretical studies of fracturing - analytical as well as numerical investigations - are classical concepts of fracture mechanics such as Griffith's energy-based description. The same is true for phase field fracture models that represent cracks by means of an additional scalar field. The evolution of this field can be found from minimization of a regularized energy functional which corresponds to a generalized Griffith criterion. This work discusses configurational forces as a means to highlight the relation between fracture evolution in a phase field model and the classical fracture mechanical concepts. In contrast to other numerical tools that rely on configurational forces to model the crack propagation, the configurational forces serve a different purpose in a phase field model for fracture. Here, they are a result of a post-processing step that enhances the understanding of the simulated fracture problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present contribution focuses on fracture caused by indentation loading on the surface of a brittle solid. Its theoretical prediction is a challenging task due to the fact that crack nucleation is not geometrically induced, but is caused by the stress concentration in the contact near-field. The application of the phase field model requires constitutive assumptions to ensure a tension-compression asymmetric material response and prevent damage in compressed regions. This is achieved at the cost of giving up the variational concept of brittle fracture. We simulate the indentation of a cylindrical flat-ended punch on brittle materials like silicate glass. In order to reduce the numerical effort, we exploit axisymmetric conditions for the finite element formulation. After crack initiation stable propagation of a cone crack can be observed in good agreement with experiments. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The aim of this study is to investigate elasticity based damage models in which the isotropic damage is driven by different history parameters under uniaxial setting. This leads to a suitable history parameter for the description of material strain-softening realistically. Existing damage evolution laws from literatures are used to compare the results using strain and energy equivalence principles. A suitable damage evolution law which is similar to Weibull's failure distribution is proposed in the framework of energy equivalence. Numerical results exhibit good agreement with experimental results. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Common cruciform specimen for biaxial tensile testing of sheet moulding compound, take damage and finally fail in uniaxially loaded areas. When using these specimen, an observation of damage initialization and failure in biaxially loaded areas is, therefore, not possible. In this paper, a parametric shape optimization is described to find a more suitable specimen shape. The parametrization of the specimen is presented. Objective functions are introduced to measure the appropriateness of specimen. A weighted summation transfers the constraint multiobjective optimization problem into a constraint scalar-valued problem. Findings of experiments suggest that a specimen shape with straight, non-tapering arms and slits along the arms is reasonable. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An application of the finite fracture mechanics concept to open-hole plates subject to combined tensile and bending loading is presented. In finite fracture mechanics, the simultaneous satisfaction of both, a stress and an energy criterion, is enforced as a condition for crack initiation. Efficient modeling and closed-form expressions for the dependence of the stress and energy quantities on governing structural and material parameters allow for a comprehensive numerical analysis of the onset of asymmetric crack patterns. The obtained failure load predictions are found to agree well with a cohesive zone model and experimental data from literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A two-dimensional model for stage I short crack propagation on multiple slip planes under the influence of hydrogen is presented. It considers elastic-plastic material behaviour by allowing sliding on the active slip planes in the corresponding slip directions. A crack propagation law based on the crack tip sliding displacement is used to simulate crack growth. The activation of slip bands and the sliding on these active slip bands will be influenced by the local hydrogen concentration. The model is solved numerically using the boundary element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This work outlines a variational-based framework for the phase field modeling of ductile fracture in elastic-plastic solids at large strains. The phase field approach regularizes sharp crack discontinuities within a pure continuum setting by a specific gradient damage model with geometric features rooted in fracture mechanics. Based on the recent works [1, 2], the phase field model of ductile fracture is linked to a formulation of gradient plasticity at finite strains in order to ensure the crack to evolve inside the plastic zones. The thermodynamic formulation is based on the definition of a constitutive work density function including the stored elastic energy and the dissipated work due to plasticity and fracture. The proposed canonical theory is shown to be governed by a rate-type minimization principle, which determines the coupled multi-field evolution problem. Another aspect is the regularization towards a micromorphic gradient plasticity-damage setting which enhances the robustness of the finite element formulation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In hydraulic fracturing, the pressure exerted by the fracking fluid onto the surrounding solid, is typically obtained from solving the Reynolds equation. This is not always robust and leads to a complex behaviour at the crack front (toughness or viscous regimes). In the presented work, the Reynolds equation is replaced by a simplified fluid model, where pre-defined pressure distributions are assumed which lead to a simpler and robust coupled problem. The surface integration of the fluid pressure onto the surrounding solid is outlined without any limitations on the distributions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A cohesive zone element technique (CZ) is applied to study grain boundary fracture in nano coating layers (see [1]). This goes along with the investigations of the delamination and fracture behavior of the coatings and the substrate interface. The main motivation is to investigate antiadhesive and wear resistant properties of coatings made of ceramics produced by the High Power Pulsed Magnetron Sputtering (HPPMS) technique [2]. Different physical conditions in HPPMS result into different grain morphologies with different mechanical properties. Therefore prediction of fracture and damage in such systems can lead to the optimum choice of process parameters in order to gain the best fracture resistance properties for the coatings. To illustrate the applicability of the model, several simulations with different mechanical and structural properties are performed. The developed CZ element model is capable of modeling the separation, the contact and also the irreversible reloading conditions in different directions [3]. The model is further developed to be applicable for geometrically complex interfaces including different bonding behaviors, with a high robustness. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The use of a common set of basis functions for design and analysis is the main paradigm of isogeometric analysis. The characteristics of the commonly used non-uniform rational B-splines (NURBS) surfaces require methods to handle non-conforming meshes to attain an efficient computational framework. The isogeometric mortar method uses constrained approximation spaces to enforce a coupling of deformations at the interface between patches in a weak manner. This method neither requires additional degrees of freedom nor the choice of empirical parameters. The main drawback of the standard isogeometric mortar approach is the non-local support of the mortar basis functions along the interface. This yields a large number of nodes per element for elements adjacent to the interface. Thus, the computational costs increase significantly for mesh refinement. This issue is remedied by the use of dual basis functions for the mortar method, which is referred to as dual mortar method. In this contribution several choices for the dual basis functions for B-splines are proposed and compared. A special focus is set on the support of the dual basis functions and on the support of the resulting mortar basis functions. Numerical examples show the influence of the choice for the dual basis functions on the accuracy of the global stress distribution, on the fulfillment of the interface conditions and on numerical efficiency. The use of approximate dual basis functions is shown to be competitive to computations of conforming meshes in terms of accuracy and efficiency. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Common material models that take into account softening effects due to damage have the problem of ill-posed boundary value problems if no regularization is applied. This condition leads to a non-unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non-local behavior of the damage [1]. For this purpose a field function is often used to couple the local damage parameter to a non-local level, in which differences between the local and non-local parameter as well as the gradient of the non-local parameter can be penalized. In contrast, we present a novel approach [2] to regularization that no longer needs a non-local level but directly provides mesh-independent results. Due to the new variational approach we are also able to improve the calculation times and convergence behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution a new specimen, which enables high precision tension-compression testing, is presented. Due to a special mounting geometry, tests from a compression strain of −45 % up to a tension strain of 400 % can be performed with a nearly homogeneous deformation field within the measuring zone. Consequently, the mechanical behavior of rubber, which exhibits phenomena like Mullins effect, Payne effect, recovery and relaxation behavior, can be characterized within experimental investigations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The main purpose of this paper is the development and implementation of a method for the reduction of the so-called locking effect in the isogeometric Reissner-Mindlin shell formulation. In [1] an isogeometric Reissner-Mindlin shell formulation with an exact interpolation of the director vector based on continuum mechanics was introduced. The numerical examples showed that the accuracy and efficiency increased. However, there are only few effective concepts for the prevention of locking effects for low polynomial degrees. In the work of Beirão da Veiga [2], shear locking is prevented for a Reissner-Mindlin plate formulation by using suitable solution spaces. Here, the method is extended to the Reissner-Mindlin shell formulation. Different control meshes are used for displacements and rotations. Furthermore, the basis functions in the direction of the relevant rotation are one degree less than the ones which are chosen for the displacements. That leads to control meshes with different number and location of the control points. The aim is to avoid shear locking due to the coupling of shear strains and curvature since the compatibility requirement for pure bending is then fulfilled. The accuracy and efficiency of this method are investigated for different examples. In addition, the results are compared to the analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution deals with a stress-displacement mixed finite element formulation for elasto-plasticity within the framework of small deformations based on the Prange-Hellinger-Reissner (PHR) functional. The interpolations for the displacements are given by standard Lagrangian shape functions and a 5-parameter discontinuous interpolation is introduced for the stresses which was published by [1]. Based on the principle of maximum plastic dissipation the flow rule and hardening law will be derived by regarding a von Mises yield criterion, see [2]. In contrast to [3], we apply a point-wise enforcement of the flow rule, hardening law and loading/unloading conditions. This work is related to the physically nonlinear mixed finite element based on the Prange-Hellinger-Reissner formulations for elasto-plasticity, [4]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We describe a novel approach to the computation of free resolutions and of Betti numbers of polynomial modules based on a combination of the theory of involutive bases with algebraic discrete Morse theory. This approach allows for the first time to compute Betti numbers (even single ones) without determining a whole resolution which in many cases drastically reduces the computation time. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: With the aim of obtaining a general local formulation for anisotropic growth in soft biological tissues, a model based on the multiplicative decomposition of the growth tensor is formulated. The two parts of the growth tensor are associated with the main anisotropy directions. Together with an anisotropic driving force, the model enables an effective stress reduction by including growth-induced residual stresses, which is demonstrated in a numerical example of an idealized arterial segment. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The SBFEM is employed for the extraction of 3D stress singularity exponents and their associated deformation modes. It makes use of a separation of variables approach, which is substituted into the virtual work equation so that only parts of the boundary need to be discretized while the 3D boundary value problem is considered analytically in a scaling variable. The enrichment of the standard separation of variables representation for the displacements with a decomposition of the analytical crack displacement field yields a substantial improvement of the method's accuracy and convergence properties. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The primary goal of this paper is to propose an alternative method for obtaining the band structures of the 3D sonic composites without/ with point defects. The point defects are vacancies or foreign interstitial atoms which are supported by the interfaces between the hollow spheres and the matrix. The proposed method is used to simulate a sonic plate composed of an array of acoustic scatterers which are piezoceramic hollow spheres embedded in an epoxy matrix. The scatterers are made from functionally graded materials with radial polarization [1, 2]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Subject of the investigation is a thick-walled cylindrically curved shell guided at the ends which is heated at its inner or outer surface. The material is presupposed to be functionally graded obeying a power law. Both the elastic limits according to von Mises and the stress distributions for different grading exponents are discussed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper is motivated by dynamic simulations of fiber-reinforced materials in light-weight structures, and has two goals. First of all, the introduction of energy-momentum schemes for nonlinear anisotropic materials, based on GALERKIN approximations in space and time, assumed strain approximations in time and superimposed algorithmic stress fields (compare [1]). Second, to show a variationally consistent design of energy-momentum schemes using a differential variational principle. We develop a discrete variational principle leading to energy-momentum schemes as discrete EULER-LAGRANGE equations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In order to consider growing expectations on vibro-acoustic performance of products within the design process, reliable simulation tools are necessary. In this paper, we present a approach for the simulation of laminated shells composed of elastic and poroelastic layers. We assume that the shell is given by a parametrization, which allows us to work witn the exact geometry. The three-dimensional problem is reduced to a two-dimensional one, by choosing a set of through-the-thickness functions for each quantity and through-the-thickness integration. The implemented high order finite element approach for the reduced problem on the reference surface relays on hierarchical shape functions. In a numerical example, we show the influence of poroelastic materials attached to a aluminium shell. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The finite cell method is based on a fictitious domain approach, providing a simple and fast mesh generation of structures with complex geometries. However, this simplification leads to intersected cells where the standard Gauss quadrature does not perform well. To perform the numerical integration of these cells, we use the moment fitting approach that generates an individual quadrature rule for every broken cell. In this paper, we will perform a non-linear optimization approach to find the optimal position and number of the integration points. The findings show that the proposed method leads to efficient quadrature rules that require less integration points than other existing integration methods. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present work deals with the design of structure-preserving numerical methods in the field of nonlinear elastodynamics and structural dynamics. Structure-preserving schemes such as energy-momentum consistent (EMC) methods are known to exhibit superior numerical stability and robustness. Most of the previously developed schemes are relying on a displacement-based variational formulation of the underlying mechanical model. In contrast to that we present a mixed variational framework for the systematic design of EMC schemes. The newly proposed mixed approach accomodates high-performance mixed finite elements such as the shell element due to Wagner & Gruttmann [1] and the brick element due to Kasper & Taylor [2]. Accordingly, the proposed approach makes possible the structure-preserving extension to the dynamic regime of those high-performance elements. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present approach deals with a numerical method for the static analysis of solids in boundary representation. A formulation is derived where the geometrical description of the boundary is sufficient to define the elastic boundary value problem for the complete solid. The interior of the domain is described by a radial scaling parameter. Following the idea of the scaled boundary finite element method [1] the scaling of the boundary with respect to a specified scaling center provides a representation for the complete solid. This concept fits perfectly to the boundary representation modeling technique, which is frequently used in CAD to define solids. In CAD the boundary of the solid is described by employing NURBS basis function. In the isogeometric analysis methodology, [2], a trivariate tensor product structure is used to analyze solids. In the present approach, the tensor-product structure of the solid will be reduced by one dimension to parameterize the physical domain, i. e., the three-dimensional solid exploits only two-dimensional NURBS objects, which parameterize the boundary surfaces. Hence, the present approach represents perfectly the isoparametric paradigm, see [3]. However, in [3] the weak form of equilibrium is enforced on the boundary surface. This leads to an ordinary differential equation (ODE) of Euler type, which could be solved by applying a collocation scheme. In the present approach the weak form is employed on the boundary and in scaling direction. The displacement response in the radial scaling direction is approximated by one-dimensional NURBS. Finally, the Galerkin projection of the weak form yields a linear system of equilibrium equations whose solution gives rise to the displacement response. In conclusion, the presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. Numerical examples will show the capabilities of the presented method. The accuracy of the method is investigated by comparison to the analytical solution. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Postbuckling responses of delaminated composite struts are semi-analytically modelled. The model used allows to describe the postbuckling behaviour beyond the state where delamination growth is initiated. In the current work, a multi-layered composite strut of differently stacked transversally isotropic unidirectional layers is investigated. A pre-existing delamination is assigned in between two layers. By using only four generalized coordinates postbuckling responses incorporating delamination growth are determined. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Aerosols are defined in the simplest form as a mixture of solid or liquid particles suspended in a gas [1]. Brake dust is an aerosol, generated as a result of erosion between brake disc and brake pad. The aerosols can cause visual disorder, heart and lung diseases, short term acute symptoms like asthma, bronchitis and long term chronic irritation and inflammation of the respiratory track, which can lead to cancer. Therefore, it is important to know which factors are affecting the erosion rate of brakes. The main objective of this work is to measure the erosion rate of brake discs and brake pads, depending on temperature changes and deformation by performing experiments and simulations at varying velocities and load conditions. The general purpose, commercially available finite element solver Abaqus is used for performing the thermomechanically coupled simulations. Archad's Wear Law is used for the wear calculation. Experiments are conducted by using a pin on disc test bench. Temperature changes are measured by using thermocouples and erosion rates by measuring the total volume loss. At the end, relationships between erosion rates and temperature changes for different brake disc velocities and load conditions are investigated and experimental and simulation results are compared and discussed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We propose an extension of the uniform approximation approach towards the simultaneous truncation of the associated dual energy. In the talk, we derive a hierarchy of approximating theories and corresponding a-priori error estimates for their solutions, for the special case of an isotropic, linear elastic, one-dimensional structural member with rectangular cross-section. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution presents a finite element appropriate for the modeling of general interfaces, incorporating normal contact conditions as well as description of the tangential interaction on the interface. The finite element is formulated as a solid element and its kinematics take into account the kinematics of both Master and Slave . A covariant approach is adopted for the exact representation of the geometry of the interface and all parameters are expressed in terms of local coordinate systems. An elastoplastic associative constitutive law assuming plastic deformations, which is numerically implemented as a frictional law describes the tangential interaction of the contact surfaces. In this way a three-dimensional Segment-to-Segment frictional contact formulation, applying an associative plasticity law instead of the Coulomb friction law is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: When bodies rotate they are subjected to velocity-dependent gyroscopic and inertia effects, which alter the dynamic behaviour of the structure. Analysing its eigenpairs consisting of eigenvalues and eigenvectors, these parameter-dependent changes can be tracked as eigenpaths by means of a continuation algorithm as in [1]. For rotationally symmetric structures an ALE approach (ALE = Arbitrary LAGRANGIAN-EULERIAN) for the finite element method as described in [2] can be employed. It allows simulating rotational influences on the body without actually having to rotate the mesh of the structure itself. This still-standing mesh facilitates further steps like coupling of other, static components with the rotating body. The combination of ALE with eigenpath analysis including an example is described in the following. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper represents an analysis of different approaches to solve a specific practical task – to find a solution of the inhomogeneous differential equation, which describes tire lateral deformation by means of the beam theory. The equation has fourth order and is linear, the inhomogeneneous part is discrete nonmonotone function. The options to substitute this function with polynomial, linear segments or Fourier series are compared concerning solution error and computation time. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A locking phenomenon can be observed in the case of anisotropic elasticity, due to high stiffness in preferred directions. In this contribution we propose a formulation with the goal to overcome this locking problem. We apply a Simplified Kinematic for the Anisotropic part of the free-energy by means of a constant approximation of the right Cauchy-Green tensor. For the tested boundary value problem the SKA-element performs excellent and behaves extremely robust. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution discusses the non-linear dynamic behaviour of a rotor system equipped with a compliant seal. The investigated model consists of a Laval -Rotor and a stiff seal ring which is visco-elastically supported. The fluid forces stemming from the turbulent incompressible lubricant film are accounted for by the non-linear Muszynska model. The added compliance leads to an improved stability behaviour of the steady state. Within the post-critical regime the additional compliance gives rise to bifurcations of the stationary vibration: Hopf bifurcations lead to limit cycles which can loose their stability via Neimark-Sacker bifurcations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution introduces the setup of a self-resonating system consisting of a freely-sliding mass over a vibrating elastic beam under harmonic excitation. Under specific operating regime, the slider shows tendency to move and adapt its position to where the whole system resonates. The behavior of the slider during that motion is investigated. Experimental observations of the operating regime dependency on some parameters are provided. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution investigates existing descriptions of electro-mechanical analogies and attempts of an extension by memristive elements. Therefore, the electro-dynamical role of memristors is analyzed and translated into the context of system dynamics. This analysis leads to a generalized classification of devices for dynamical systems with a single degree of freedom (SDOF). (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper discusses stationary rotordynamics of synchronous electric machinery, considering different load cases. The model comprises the electrical operation in a rigid network and in an isolated condition. The mechanical part is modelled as a Laval Rotor (Jeffcott Rotor) with a noncircular shaft, accounting for both static- and dynamic rotor eccentricities. The results show, that the machine's electrical operation may influence the occurence of mechanical vibrations significantly and therefore demonstrate the importance of analysing the electromechanical interaction. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A flexible finger with muscles made of Nitinol wires and the skin made of auxetic material is analyzed from the tactile sensing point of view. The recognizing of the shape and texture of 3D objects is performed by simulation the action of an array of nanopiezotronic transistors integrated into the skin. The array of nanopiezotronic transistors makes possible the detection of the pressure-induced changes in the auxetic skin. The shape and texture of the objects is best estimated by determining the surface and texture as an n -ellipsoid defined by 12 parameters. An inverse problem is solved in order to find these parameters from the condition that the n -ellipsoid best fits the set of data points probed by touch with the finger. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A rotor partially filled with a viscous incompressible fluid is modeled as planar system. Its structural part, i. e. the rotor, is assumed to be rigid, circular, elastically supported and running with a prescribed time-dependent angular velocity. Both parts, structure and fluid, interact via the no-slip condition and the pressure. The point of departure for the mathematical formulation of the fluid filling is the Navier-Stokes equation, which is complemented by an additional equation for the evolution of its free inner boundary. Further, rotor and fluid are subjected to volume forces, namely gravitation. Trial functions are chosen for the fluid velocity field, the pressure field and the moving boundary, which fulfill the incompressibility constraint as well as the boundary conditions. Inserting these trial functions into the partial differential equations of the fluid motion, and applying the method of weighted residuals yields equations with time derivatives only. Finally, in combination with the rotor equations, a nonlinear system of 12 differential-algebraic equations results, which sufficiently describes solutions near the circular symmetric state and which may indicate the loss of its stability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: High-frequency vibrations have been shown to smooth the effective characteristics of dry friction and may be used in order to quench undesired phenomena such as friction induced vibrations. Recent contributions have discussed the influence of contact compliance on vibrational smoothing. Within this contribution, an experimental set-up is presented, which has been developed in order to validate the calculated results. After a brief description, some general properties of the system are investigated, including stationary and oscillatory behaviour. Without vibrational excitation, friction induced vibrations occur at low sliding velocities. The corresponding motion of the system is analysed and compared to the results of FE-based simulations. Finally, a first attempt is presented reducing the average friction force by imposing appropriate vibrations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Due to the exponential growth in computing power, numerical modelling techniques method have gained an increasing amount of interest for engineering and design applications. Nowadays, the deterministic finite element (FE) method, an efficient tool to accurately solve the Partial Differential Equations (PDE) that govern most real-world problems, has become an indispensable tool for an engineer in various design stages. A more recent trend herein is to use the ever increasing computing power incorporate uncertainty and variability, which is omnipresent is all real-live applications, into these FE models. Several advanced techniques for incorporating either variability between nominally identical parts or spatial variability within one part into the FE models, have been introduced in this context. For the representation of spatial variability on the parameters of an FE model in a possibilistic context, the theory of Interval Fields (IF) was proven to show promising results. Following this approach, variability in the input FE model is introduced as the superposition of base vectors, depicting the spatial ‘patterns’, which are scaled by interval factors, which represent the actual variability. Application of this concept, however, requires identification of the governing parameters of these interval fields, i. e. the base vectors and interval scalars. Recent work of the authors therefore was focussed on finding a solution to the inverse problem, where the spatial uncertainty on the output side of the model is known from measurement data, but the spatial variability on the input parameters is unknown. Based on an a priori knowledge on the constituting base vectors of the interval field, the simulated output of the IFFEM computation is compared to measured data, and the input parameters are iteratively adjusted in order to minimize the discrepancy between the variability in simulation and measurement data. This discrepancy is defined based on geometric properties of the convex sets of both measurement and simulation data. However, the robustness of this methodology with respect to the size of the measurement data set that is used for the identification, as yet remains unclear. This paper therefore is focussed on the investigation of this robustness, by performing the identification on different measurement sets, depicting the same variability in the dynamic response of a simple FE model, which contain a decreasing amount of measurement replica. It was found that accurate identification remains feasible, even under a limited amount of measurement replica, which is highly relevant in the context of a non-probabilistic representation of variability in the FE model parameters. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar function as it is common in level set based methods. Hence, the interface is not aligned with the mesh. An unfitted finite element discretization based on a Taylor-Hood velocity-pressure pair and an XFEM (or CutFEM) modification is used for the approximation of the solution. This allows for the accurate approximation of solutions which have strong or weak discontinuities across interfaces which are not aligned with the mesh. To arrive at a consistent, stable and accurate formulation we require several additional techniques. First, a Nitsche-type formulation is used to implement interface conditions in a weak sense. Secondly, we use the ghost penalty stabilization to obtain an inf-sup stable variational formulation. Finally, for the highly accurate approximation of the implicitly described geometry, we use a combination of a piecewise linear interface reconstruction and a parametric mapping of the underlying mesh. We introduce the method and discuss results of numerical examples. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Finite element simulations are commonly used to investigate the soil-structure interactions of mechanised tunnelling processes, such as to provide predictions on the expected surface settlement field. For real-time predictions during the tunnel construction, the finite element model is substituted by a hybrid surrogate model combining Artificial Neural Network and Proper Orthogonal Decomposition approaches. The surrogate model is employed to predict time-variant interval surface settlement fields for selected scenarios of the tunnelling process steering parameters in real-time considering uncertain geotechnical parameters as intervals. For this purpose, the surrogate model in [1], which is based on a Recurrent Neural Network and Gappy Proper Orthogonal Decomposition technique, is split into surrogate models for midpoint and radius computations of the interval data. The online computation time of the new surrogate modelling approach is only a few seconds, which enables tu apply it for real-time predictions and to support the Tunnel Boring Machine steering. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using two time grids consisting of micro and macro nodes. This formulation can be extended for multi-body systems. The rigid multi-body system is described by the so called director formulation and constraints describing the joints connecting the bodies. With the Lagrange multiplier method, the constraints are introduced into the equations of motion. A way to implement the null space method into the variational multirate framework is shown and the influence on the number of unknowns is investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Dynamic stability of a milling process with varying workpiece dynamics is investigated. The milling tool moves along the workpiece with a prescribed feed rate, whereby the contact point shifts. Furthermore, the workpiece dynamics is affected by material removal. The resultant varying workpiece dynamics is taken into account by parametric model order reduction including modal truncation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We present a recent result on null controllability of one-dimensional linear parabolic equations with boundary control. The space-varying coefficients in the equation can be fairly irregular, in particular they can present discontinuities, degeneracies or singularities at some isolated points; the boundary conditions at both ends are of generalized Robin-Neumann type. Given any (fairly irregular) initial condition θ 0 and any final time T , we explicitly construct an open-loop control which steers the system from θ 0 at time 0 to the final state 0 at time T . This control is very regular (namely Gevrey of order s with 1 〈  s  〈 2); it is simply zero till some (arbitrary) intermediate time τ, so as to take advantage of the smoothing effect due to diffusion, and then given by a series from τ to the final time T . We illustrate the effectiveness of the approach on a nontrivial numerical example, namely a degenerate heat equation with control at the degenerate side. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Soft tissues can be considered as a composite material where a matrix (ground substance) is reinforced by collagen fibers. These fibers consist of fibrils, which are connected by proteoglycan (PG) bridges. The time-dependent properties of soft tissues appear to be mainly caused by proteoglycans [3]. This contribution presents a modeling approach where damage in the PG bridges arises due to the failure of the covalent bonds between two proteoglycans. The breakage of covalent bonds is reversible over time and incorporated using a healing formulation. A high PG density supports interfibrillar sliding and hence leads to a lower fibril stretch [8]. Accordingly, the damage propagation in PG bridges leads to a higher stretch in the fibrils and therefore to a stiffer material response. The strain energy of the fibrils is based on the response of single tropocollagen molecules and takes both, an entropic and an energetic regime into account [5]. Finally, the model is compared against experimental data available in the literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In recent years, femoroacetabular impingement (FAI) has become increasingly common. As published in the literature, FAI is caused by an unphysiological contact between the proximal femur and the acetabular rim, which may lead to pain, limitation of movement, and damage of cartilage. In this paper, patient-specific finite element simulations of the movement of the hip based on gait motion data and MRI segmentation were conducted to check stresses of the acetabulum and femur, and additionally whether a bony contact is present or not. The study's findings show no bony contact between femur and acetabulum, which may lead to the hypothesis that the labrum and its deformation and/or the articular capsule are involved in the mechanism of FAI. In order to verify this hypothesis more simulations including labrum and capsule must be performed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Proximal femur fractures are very common injuries especially among older patients. Although, there are various alternatives and improvements in implant design and operating techniques, the treatment still represents a big medical challenge. Therefore, the understanding of crack initiation and propagation in the proximal femur is of great interest. The objective of this work is to present a simplified phenomenological model that is able to predict crack initiation and propagation in the proximal femur. This will be simulated by using a phase-field modelling (PFM) approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: There exist many different approaches investigating the contraction mechanisms of skeletal muscles. Thereby, the mechanical behavior, such as force generation in association with kinematic and microstructure, play an important role in modeling of muscle behavior. Besides the mechanical behaviour, the validation of muscle models requires the geometrical environment, too. The geometry of a muscle can be divided into macrostructure, existing of aponeurosis-tendon-complex (ATC) and muscle tissue (MT), as well as the fascicle architecture, representing the microstructure of the MT. In this study, the macrostructure of the isolated M. gastrocnemius was observed during isometric contraction by using three-dimensional optical measurement systems in combination with mechanical measurement techniques. The surface deformation was reconstructed at specific force and length relationships and further the muscle tissue, aponeurosis, and tendon were distinguished, building up a macroscopic geometrical dataset. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Tendon injuries are a common problem in medicine. While healthy tendons do not rupture, tendon injuries are mostly accompanied by pathological changes and microruptures. Unfortunately, still less is known about the underlying processes. Thus, in the present study, we introduce artificial damages into native tendon tissue and investigate its mechanical behaviour experimentally. In the second part of this study, we propose a theoretical model for predicting the mechanical behaviour of the damaged tendon and present its validity. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A gradient-extended damage-plasticity model is discussed which is based on a micromorphic approach according to Forest [1]. Damage and plasticity are treated as independent but strongly coupled dissipative phenomena by considering separate yield and damage loading functions to describe the onset of plastic flow and / or damage evolution. A numerical benchmark test conducted in the study reveals that the model is able to essentially cure the well-known mesh-dependence issue which is known from finite element simulations involving conventional (i. e. ‘local’) damage material models. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The urinary bladder is characterised by its ability to withstand high deformations under harsh chemical conditions. Occurring irregularities in the bladder wall disturb the correct functioning during storage and release. In order to support the development of effective therapeutic treatments for dysfunctional urinary bladder a theoretical model was developed. Accounting for different pathways of smooth muscle activation the proposed model is based on a coupled electrical-chemical-mechanical approach. Finally, the model is implemented in the finite-element framework to consider complex geometries and boundary conditions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Replacement tissues, designed to fill in articular cartilage defects, should exhibit the same properties as the native material. The aim of this study is to foster the understanding of, firstly, the mechanical behavior of the material itself and, secondly, the influence of cultivation parameters on cell seeded implants as well as on cell migration into acellular implants. In this study, acellular cartilage replacement material is theoretically, numerically and experimentally investigated regarding its viscoelastic properties, where a phenomenological model for practical applications is developed. Furthermore, remodeling and cell migration are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A relation is established between a recently proposed single-phase model for human amnion [1], in which an internal state variable accounts for viscoelastic volume changes due to fluid outflow, and an explicitly bi-phasic representation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase-field fracture approach for finite deformations, see [4]. A phase-field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. In order to improve the accuracy, a fourth-order Cahn-Hilliard phase-field equation is considered, requiring global C 1 continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase-field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the development of new biaxially loaded specimens to study the damage behavior of ductile metals under different loading conditions. Based on numerical simulations newly designed biaxial specimens are developed and numerically studied while an experimental program has been realized in continuation. The experimental results have been evaluated by digital image correlation (DIC) and compared with the results of finite element simulations. By concideration of different biaxial loading conditions it is possible to cover a wide range of stress triaxialities and Lode parameters in tension, shear and compression domains and consequently the newly proposed specimens facilitate a controlled study of damage and fracture at different stress states. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The human liver is important for hepatic metabolism regulations which depend on complex and time depending biochemical reactions coupled to the hemodynamic blood perfusion. Growth effects can impair the perfusion and therefore affect the metabolism. Such influences can be observed during the accumulation of fat in the liver tissue. The fat accumulation results from the lipid metabolism which comprises synthesis and degradation of lipids in liver cells. Individual addictions to alcohol and high fat diets are possible causes which result in an excessive synthesis of lipids. The liver sensitively reacts to such changes which could affect the viability of the organ. To observe these coupled influences of perfusion-metabolism-growth effects we use a computational model with a multi-component/tri-phasic/bi-scale approach to simulate the functionality of the human liver with respect to fat deposition. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This numerical study investigates the effects of fatigue material data and finite element types on accuracy of residual life assessments under HCF conditions. The bending of cross-beam connections is simulated in ANSYS Workbench for three different combinations of beam profiles. The weldments are made of the high-strength steel grades C350LO and C450LO according to AS3678. The stress analysis of weldments is implemented with solid and shell elements using linear material and geometry consideration. The stress distributions are transferred to the embedded fatigue code nCode DesignLife. For both variants of FE-mesh, the nominal stress in the weld toes is extracted by splitting the total stress into membrane and bending components and filtering out non-linear component. Considering the effects of bending, size and mean stress, failure locations and fatigue life are predicted using the Volvo method and rules from ASME BPV Code. Three different pairs of experimental S-N curves (stiff and flexible) are used as material data input for fatigue analysis. The obtained numerical predictions are compared to the experimental results for shell FE-models. The predictions using the S-N curves for an equivalent steel demonstrate the best accuracy proving the fact that specific material data input is more effective than a generic data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present work discusses numerical results of damage evolution due to thermoshock processes at refractory ceramics. Damage patterns have been generated using a two-scale approach for brittle materials, implemented into a finite element framework. For this purpose, a cell model has been employed, incorporating cracks on a microscopic level. The impact of these discontinuities on macroscopic material properties and damage evolution is determined with the help of analytical homogenization techniques. Finally, the potential of the numerical tool is demonstrated by means of refractory bricks, being imposed by thermomechanical loading. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Natural fiber reinforced bio-polymers are in the focus of many research projects to understand and improve the mechanical behavior subjected to different process parameters during production. To provide safe and reliable light weight constructions, special interest is directed towards the damage and fracture behavior of such composite materials. Here, the material's behavior at the imperfect material interface between fiber and matrix plays an essential role and governs inelastic effects at the interfaces on the one hand, and the behavior of growing cracks on the other. The reduction of the elastic potential is related to both energy consuming processes in the system and in general is going along with a reduction of the crack tip loading and a shift of the crack growth direction. In this paper, the crack tip loading analysis in structures with perfect and imperfect material interfaces is presented and applied to different specimens. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)