ALBERT

Description: We study the zero dynamics and funnel control for linear passive electrical circuits. We show that asymptotic stability of the zero dynamics can be characterized by criteria on the circuit topology. Thereafter we consider the output regulation problem for electrical circuits by funnel control. We show that for circuits with asymptotically stable zero dynamics, the funnel controller achieves tracking of a class of reference signals within a pre-specified funnel. This result can be relaxed to the case of non-autonomous zero dynamics by requiring the reference trajectory to evolve within a certain subspace. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents a new approach for analysis and controller design for nonlinear descriptor systems. Thereby, we assume that the descriptor system is given in semi-explicit form and has a continuously differentiable solution, which are very mild assumptions and are fulfilled for most practical applications. Based on the known coupling controller design we transfer the analysis and synthesis from the descriptor system to an equivalent system in state-space form. Methods like dynamic and static input-output decoupling, input-output linearization, model-based feedforward-controller design, zero dynamics, exact descriptor linearization, linear time variant Riccati control, and causal observer design have been introduced based on the coupling procedure [9]. In the following, we summarize the new approach and an algorithm to compute the required state-space system. Additionally, a short introduction how to use it for decoupling control, Riccati control, and causal observer design is given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Linear dynamical systems with an affine parameter dependence producing low-rank variation in the state matrix can be recast as a nonparameterized system operating in parallel with a parameterized feed forward term operating under output constraints. This mapping permits the application of standard (nonparametric) model reduction strategies to solve parameterized problems. We demonstrate the approach on a parameterized vibration problem using optimal tangential interpolation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Different variants of the eXtended Finite Element Method (XFEM) have developed over the last years: The original, shifted, corrected, stable, and intrinsic XFEM. Herein, these variants are compared in terms of convergence rates and conditioning of the resulting systems of equations. Optimal convergence rates are achieved by the corrected, stable, and intrinsic XFEM for general enrichments. The original and shifted XFEM achieve optimal rates for selected enrichments only. In terms of the conditioning, it is found that the stable XFEM can be “optimal” in the sense that the same dependency on the mesh size as for the classical FEM is maintained. However, this finding only holds if one enrichment term is involved. In the presence of several enrichment terms, only the intrinsic XFEM yields well-conditioned systems of equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We study controllability of switched DAEs and formulate a definition of controllability in the behavioral sense. In order to characterize controllability for switched DAEs we first present new characterizations of controllability of non-switched DAEs based on the Wong-sequences. Afterwards a first result concerning the single-switch case is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In 2009, the BEM-based FEM was introduced as an numerical approach for the treatment of boundary value problems. It is a Finite Element Method (FEM) that uses Trefftz-like basis functions which are defined to fulfil the underlying differential equation locally and which are treated by means of Boundary Element Methods (BEM). Due to the implicit definition of basis functions, this approach is applicable on general polygonal and polyhedral meshes and yields conforming approximations. The elements of the discretization do not necessarily have to be convex. After a review of the recent development of higher order basis functions the method is applied to a model problem on a sequence of meshes with L-shaped elements. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Designing whole machines or processes you may need both, an integrated dynamic simulation of all components on system level and a detailed analysis of how the macroscopic behavior of a component depends on geometry and material parameters. The former analysis is usually based on systems of differential algebraic equations representing a component by not more than a few hundred states and requires tools like Matlab-Simulink® or Dymola®. The latter analysis solves discretized partial differential equations with several 100,000 degrees of freedom using finite element software like Ansys® or Comsol®. Model reduction bridges the gap between the two worlds providing small state space models with approximately the same input-output behavior as the original large finite element models. Building systems from generic components, e.g. a gas transport network from pipeline models with variable length, or optimizing the design of a device with respect to mechanical or thermal properties, we need parametric reduced models. The idea is to reduce FE models offline for selected parameter sets and to generate models for new parameters by cheap interpolation rather than expensive reduction. The different approaches to parametric linear model reduction may be divided into three classes [1]. Interpolation of transfer functions is well suited for parabolic or highly damped hyperbolic problems. However, poles are duplicated rather than shifted, which is unacceptable for weakly damped hyperbolic problems like in mechanics. The second class of methods look for a basis of state space covering system behavior over the full range of parameters. They share the critical assumption that number and meaning of states do not change with the parameters. In terms of finite elements this means that the meshes for different design parameters are morphed variants of the same reference mesh.This may become a severe restriction in practice when automatic meshing is to be applied to complicated geometries. Therefore, we propose a method from the third class, which is based on interpolating reduced system matrices [2]. Only those parts of the mesh need to share a constant topology where nodal inputs are applied and outputs are collected. The inner mesh, however, may change for different parameters. The main challenges arise from the fact that state space representations of a system are unique only up to a change of basis and that interpolating matrices which refer to non-fitting bases may cause arbitrary errors. In the article we will show how problems like leaving and entering modes or eigenvalue crossing can be overcome by using normal forms and eigenvalue tracking in parameter space. The method, which is implemented in the Fraunhofer Model Reduction Toolbox, is applied to a parametric model of a mechanical device the eigenfrequencies of which have to be kept away from some dominant excitation frequencies. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the view of robotics or granular media mechanics, we ask for the statement of the dynamical evolution problem for multibody systems with contacts and friction. The “event driven” approach does not allow to state an evolution problem in a systematic way: it gives a peculiar status to the instants of impact and to the contact points although they are unknowns of the problem. This matter of fact has given rise to a new approach in the frictionless case [4, 6] we generalize to the case including friction. Following to the point of view of Lagrange on the equation of the dynamics, we emphasize the systematic use of virtual powers and duality. This bias suggests to put emphasis on generalized reaction forces in the statement of the evolution problem and not on local reaction forces of the real world. This point of view allows to escape from pathologies e.g. Painlevé paradox [5] and Kane Paradox [3]. The proposed evolution problem accounts for impacts and friction in case of multiple unilateral constraints. We prove the existence and uniqueness of the solution to the associated rate problem. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Ancorsteel1000C is commonly used for important components including bearing rollers, gears, connecting rods, wheels and rails; most failures of these components are caused by rolling contact fatigue (RCF). In this study the fatigue damage indicator based on Fatemi-Socie critical plane were determined in a local hot spot area in finite element (FE) model in case of Hertzian stress with zero slip condition. The simulation results compared with respect to experimental data, which is in good agreement. Therefore, this approach can be implemented as a useful tool for lifetime calculations in RCF in the process of structure fatigue design. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents selected results of experimental tests carried out on the three-storey plate-column structure, which is a physical model of a building. On the top floor the semi-active tuned mass damper (STMD) is installed. That device is a kind of harmonic oscillator with a variable stiffness characteristic. The tuning of STMD is possible in the frequency range from 0 to 5 Hz, which allows to counteract the resonant vibration of plate-column structure for the three basic frequencies. The model's vibration are kinematically excited by using the earthquake simulator. It is assumed that during an experimental tests the plate-column structure's vibration are only excited by horizontal component of base motion (dominant influence on building's vibration). The aim of the experimental analysis presented in this paper is to verify the effectiveness of the semi-active tuned mass damper in vibration's amplitude reduction of the main structure. The tested device is prototype of STMD, which uses a competitive constructional solution of stiffness parameter control. By reason of above, special attention is focused on the testing of vibration eliminator in two aspects: change of stiffness characteristic (the rate of change), and the accuracy of tuning to the resonant frequencies. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In structural dynamics the initial boundary value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements. For the temporal discretization two classes of Runge-Kutta methods and the generalized-α method are compared. The representatives for the Runge-Kutta methods are diagonally implicit Runge-Kutta schemes (DIRK) and diagonally implicit Runge-Kutta-Nyström schemes (DIRKN). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper deals with a GALERKIN-based multi-scale time integration of a viscoelastic rope model. Using HAMILTON's dynamical formulation, NEWTON's equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined by a first order ordinary differential equation in time. The corresponding multi-scale time-integration is based on a PETROV-GALERKIN approximation of all time evolution equations, leading to a new family of time stepping schemes with different accuracy orders in the state variables. The resulting nonlinear algebraic time evolution equations are solved by a multi-level NEWTON-RAPHSON method. Realizing this transient numerical simulation, we also demonstrates a parallelized solution of the viscous evolution equation in CUDA©. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, the kinematic performance of flexure hinges and compliant mechanisms calculated by conventional modeling techniques are compared. As these exhibit certain drawbacks with regard to control strategies, mainly large number of degrees of freedom or unacceptable errors, a novel modeling approach for flexure hinges is presented. Instead of the entire flexure hinge only its significant regions are modeled by 3-D structural solids. These master patterns are positioned appropriately and connected by rigid constraint conditions to build a compliant mechanism. The resulting model is characterized by considerably fewer degrees of freedom than a full solid model as well as a marginal deviation of the deflection compared to that of pseudo-rigid-body models, 3-D tapered finite beam elements and analytical Timoshenko beam theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents a time integrator, which is based on a time discrete spatially weak finite element formulation, but fulfills the same balance laws as the underlying (five) differential equations. Namely, in addition to the balances of linear and angular momentum as well as entropy, also the balances of total energy and LYAPUNOV function are fulfilled. The spatially weak formulation is obtained by integration by parts. Where the resulting virtual stress power term is well-known, the virtual entropy production by conduction of heat is less known. The time discretisation is based on the midpoint rule and non-standard time discrete differential operators. This time integrator is a further development of the TC integrator of I. ROMERO. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: At the Helmholtz-Zentrum Dresden-Rossendorf an experimental plant is developed to investigate the formation of magnetic fields in flows of liquid metals. Because of the enormous hazard potential of the used liquid sodium it is essential to avoid any damages during operation and so a detailed analysis using the finite element method is necessary considering the various mechanical and thermal loads. Therefore several tens of thousands load cases have to be taken into account. Hence an algorithm is developed to identify the relevant stresses referring to FKM guideline which are used for the static and fatigue strength assessment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites which consists of a piezoelectric module enclosed by an adhesive layer which in turn is surrounded by two metal sheets. A short survey on the neccessary experimental investigations to characterise the adhesive's material behaviour is given and important aspects on the corresponding phenomenological modelling approach are presented. Both steps take into account the curing reaction, changes of volume, like chemical shrinkage, and inelastic mechanical behaviour which is temperature and curing dependent. Finally, the simulation strategy for the modelling within a finite element environment is depicted. By this, residual stresses, secondary deformations and loads on the piezo modules can be predicted, which is exemplified by a comparative study verifying a novel manufacturing strategy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Increasing requirements on the durability of road pavements demand the conception of innovative asphalt types. Particularly the stability under load needs improvement in order to prevent rutting. Since the load bearing capabilities of asphalt are mainly governed by the granular lattice and the binder that glues the rocks together, simulation based approaches that aim on supporting R&D in road engineering must capture the granulometry of the material. A Voronoi tesselation based description of the structure is proposed that enables the separate modelling of grains and binder as continuous materials and attempts to accurately reproduce those features. First, a neat Voronoi tesselation is created within the modelling domain. These irregular convex polyhedra representing the grains are subsequently subject to a shrinking process and further modified to accurately represent the granulometric distribution of real asphalt types. Now, the space between the grains can be used for a volumetric representation of the binder. Full-field strain measurements during the indirect tensile test of mastic asphalt, stone mastic asphalt and asphalt concrete have been performed for validation of the approach. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The following contribution focuses on the FEM-simulation of “Die-Less-Hydroforming” using LS-DYNA. That specific forming technology is used to create structures by inflating initial seal-welded flat 2D blanks as well as 3D hollow bodies without using any die, mould or punch in contrast to conventional hydroforming (e.g. tube hydroforming or hydromechanical deep drawing). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We discuss the infinite time-horizon linear-quadratic optimal control problem for differential-algebraic equations. In contrast to previous approaches we do not impose any assumptions on the system except for impulse controllability. In particular, we show that the optimal control problem is feasible if and only if a dissipation inequality has a solution. Moreover, we discuss conditions under which the problem has a minimizing (instead of only an infimizing) solution and furthermore, when this minimizing solution is unique. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Topology optimization techniques are applied in most cases for static applications. However, recently topology optimization procedures for structures under dynamic loads have been the focus of several studies. In this work, a topology optimization scheme for flexible multibody systems using equivalent static loads and displacement fields is investigated. The optimization problem is formulated using a homogenization method, more precisely, the solid isotropic material with penalization (SIMP) approach. The objective function in the optimization problem is the compliance and the method of moving asymptotes is used as optimizer. The objective function and the sensitivities are computed directly from the displacement field computed in the dynamic simulation. The examples of a 2-arm manipulator and a slider-crank mechanism are presented and the results are discussed to verify the improved dynamical behavior through this optimization method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For the dynamic response of multilayer sheet structures it is important to take nonlinear contact and friction forces between the layers into account. The nonlinearities inside the joints can significantly influence the dynamic behavior of the entire structure. For the dynamic analysis of such structures conventional computational approaches have an unbalanced ratio between computational time and accuracy. In order to overcome this problem, so-called “Joint Interface Modes” (JIMs) are used. These JIMs, which are problem-oriented trial vectors, extend the reduction base of classical trial vector based reduction methods. In this contribution a new calculation approach for JIMs based on trial vector derivatives is introduced. The result quality of the presented method is comparable to the direct finite element method but the computational effort is extremely low due to model order reduction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper discusses the refinement of multibody models by integration of flexible bodies and by considering nonlinearities from contacts. It presents common approaches for contact modeling in multibody simulations and strategies to include flexible bodies. A contact model is implemented in the elastic multibody model. Experimental results show that significant effects of system dynamics can be modeled by use of a multibody model including elastic bodies and contacts. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this work, the nutation momentum acting upon the Earth from the Moon's perigee mass that has not been taken into account in the Earth's precession-nutation theory was revealed. This missing momentum exhibits itself in the so-called “local latitude variation” with the Chandler's period. The results of our work raise the question of updating the Earth's precession-nutation theory and revising some postulates of the time service, astronomy, geophysics, satellite navigation, etc. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In underactuated dynamical systems, the number of control inputs n u is smaller than the number of degrees of freedom n q . Real world examples include e. g. flexible robot arms or cranes. In these two exmples the goal is to prescribe the trajectory of an end effector and find the necessary control variables. One approach to model these problems is to introduce servo constraints in the equations of motion that enforce a given trajectory for some part of the system [1]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the context of multibody simulation (MBS) system parameter identification within acceptable time can be challenging. One main difficulty is the huge amount of degrees of freedom in multibody systems and therefore the large number of dependent variables. The present work deals with the evaluation of different approaches that can be applied to typical parameter identification problems in MBS. A very powerful possibility is given by the adjoint sensitivity analysis that allows to reduce the computation effort dramatically. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The investigated multibody dynamics involve perfectly elastic, partially elastic and perfectly plastic contacts and a structure preserving approach is used in forward dynamics and optimal control simulations. The applied mechanical integrator is based on a constrained version of the Lagrange-d’Alembert principle and it represents exactly the behaviour of the analytical solution concerning the consistency of momentum maps and symplecticity: it is called symplectic momentum scheme. To guarantee the geometric exactness during the establishing or releasing of contacts, the non-smooth problem is solved including the computation of the contact configuration, time and force, instead of relying on a smooth approximation of the contact problem via a penalty potential. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The usage of flexible bodies in Multibody simulations (MBS) has widely increased their industrial application. Finite Element (FE) models with up to 10 million degrees of freedom (DOF) and some hundred million nonzero matrix entries are used to describe the flexible bodies. Before such a model can be included into an MBS, the number of DOF must be reduced to an appropriate size. Using modal reduction often the critical issue arises which modes to choose while Component Mode Synthesis based methods often lead to a relatively big size of the resulting model. Alternative methods using Moment Matching and Balanced Truncation can result in a smaller size while still remaining accurate enough. Sometimes these matrices are so huge that they can not even be stored in one computers main memory. The calculation of the necessary orthogonal Krylov subspaces needs an LU factorization which is also very memory intensive. To meet these requirements, distributed computation is used which also shortens the computational time of the reduced process. In this work, an industrial relevant FE model is reduced to a much smaller size using alternative methods. Accuracy is verified by comparing the frequency response in a defined frequency range of the original and the reduced model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effect that passive joints have on the mobility of the mechanism. Then, if the mobility, considering passive joints only, is not zero we find a condition for which the parallel manipulator is conditionally equilibrated with respect to a specific external force. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this article the authors outline how systematic multi-body equations can efficiently be used to derive a model for the design of a nonlinear vehicle dynamics controller for truck-semitrailer combinations, steering the last trailer axle. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An automotive suspension system represents one of the most complex and important systems in a passenger vehicle, which has to ensure a robust and optimized contact between the wheels and the road at any time. For improving a suspension system it is important to take an investigative look at the interaction between suspension, tire and road dynamics. Thus a part of a study into aspects of suspension modeling on multi-body simulations of rear multi-link suspension system dynamics with focus on the tire footprint area is presented in this work. (© 2014 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 a time grid consisting of micro and macro nodes. This leads to computing time savings, however not unlimited, for a certain number of micro steps per macro step the computing time is minimal. To find a relation between this minimum computing time and the number of variables in the system, the computing time for the Fermi-Pasta-Ulam problem (FPU) is measured for different numbers of masses and different numbers of micro steps. In addition, the numerical convergence of the variational multirate integration is shown for the FPU. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present paper, a new formalism for obtaining the kinematical equations of a rigid body motion is proposed. It is based on an alternative parameterization of the Lie group SO(3). Here we provide a new description of attitude kinematics by means of decomposing an arbitrary rotation into a pair of successive rotations about a fixed axis û and a varying one v̂ , which is perpendicular to û . Then û , v̂ and û × v̂ constitute a basis, in which it is most natural to obtain the kinematic equations. The latter appear to be quite simple when they are expressed in terms of the vector-parameter provided that the rotation about the fixed axis is applied first (in the body reference frame). The procedure is illustrated in different situations, in which explicit solutions are available. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The phenomenon of self-locking can be found in many technical applications and common machine parts, such as screws, chocks, and funnels. Despite this, research into this topic is mostly limited to specific applications (e.g., worm gears, screws, kinematic chains). Current works with a general scope are rare. This paper addresses the analysis of self-locking in different, two-dimensional, multibody systems, and shall contribute towards a more general analysis. To elaborate on the characteristics of self-locking, the effect is first shown and explained using simple systems as examples. From these examples, an approach towards a generalized description of self-locking is proposed, which is used as a foundation for the development of two identification methods. The analysis of the self-locking mechanism in multibody systems is realized first through an analytical ansatz, and then using a numerical simulation of the examples shown. The analytical and numerical analyses of the systems deliver a criterion, and respectively an algorithm, which enables the identification of self-locked assemblies in different systems of multiple bodies. The algorithm is designed to identify self-locking during integration of the equations of motion, whereas the analytic criterion is formulated for static systems with known, increasing external loads. The results of the two analysis methods correspond very well for the given example systems, leading to the conclusion that both methods are equivalent and usable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Growth in living materials is the result of the changes in volume and mass during their development. If volume expansion occurs in a constrained case, some living materials change its growth behaviour. For example, when growth takes place in an environment with restrictions of volume, living materials will stop their volume expansion under compression due to the high amount of water that makes these bodies nearly incompressible. In case boundary conditions limit the growth of the body, the growth direction changes and gives the body another shape as expected. We present a modelling approach that takes volume and shape restrictions during growth into account. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The development of the human brain with its characteristically folded surface morphology remains an intensively discussed topic. Impressive advancements in different fields of research have enhanced the understanding of the brain. However, the mechanism that underlies the folding process in healthy and diseased brains remains undetermined. Here, we hypothesize that growth induced mechanical instabilities drive folding. Using the nonlinear field theories of continuum mechanics supplemented by the theory of finite growth [1], we model the human brain as a bi-material with the cerebral cortex, a morphogenetically growing outer layer of gray matter, and the subcortex, a strain-driven growing inner core of white matter [2]. This approach integrates the two popular but competing hypotheses that cortical folding is either driven by differential growth or by axon elongation. Through systematic sensitivity analyses, we identify the critical process parameters of cortical folding and quantify their impact on brain morphology. We further simulate phenomena causing malformations like lissencephaly and polymicrogyria [3], which are associated with neurological disorders, including severe retardation, epilepsy, schizophrenia, and autism. Understanding the mechanisms of cortical folding during brain development might facilitate the diagnostics and treatment of malformed brains. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution deals with the modeling of the physiological behavior of arterial walls, in order to enable a reliable calculation of the transmural stress distribution including also the active response of arterial tissue. Therefore, a simple viscoelastic model, which only requires few material parameters, is considered. Furthermore, a comparative study, investigating the influence of viscoelasticity on the mechanical behavior of arterial walls, is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This study focuses on a formulation within the theory of porous media (TPM) for continuum multicomponent modeling of osmotic driven deformation in articular cartilage. The cartilage consists of porous solid matrix (extracellular matrix(ECM)),which is reinforced by collagen fibers and saturated by a fluid phase. The solid and fluid phases are considered as immiscible constituents occupying spatially their individual volume fraction. However, both phases include electrolytes, which are responsible for the osmotic pressure. The collagen fiber induce both, a transverse-isotropic stress and permeability behavior which is represented in the modal approach by an invariant-based description for the stress and anisotropic permeability tensor for the fluid flow, respectively. The osmotic pressure is captured by considering the electro-chemical potential of the electrolytes. After discussing the main details of the large-strain coupled poro-osmotic-hyper-elastic model approach, a brief numerical example is given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Long-term studies reveal that mechanical stimulation causes growth and remodeling phenomena within biological tissues. The main aim of this research is to fully understand and control these phenomena. For accomplishing that, two steps are considered: first, we determine a suitable numerical model based on different approaches by a comparative study using experimental validations, and second, investigate the mechanical properties of the tissue specimens after a remodeling process. We start with the first step by choosing a convenient model that mimics the biotissue for running the numerical simulations in the second step. There are different models available that determine the mechanical properties of soft replacement tissues seeded with human chondrocytes in modern medical applications. It is our objective to achieve a common methodology of theory and experiments that allows the determination of the mechanical properties of the native material. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The stability of the human spine is highly dependent on the cancellous bone structure of the vertebra. In the case of osteoporosis and accompanied weaking of the vertebral structure, compression fractures and other lesions of the affected patient may occur. The reinforcement of the porous cancellous bone by the injection of bone-cement is a common procedure in order to overcome this issues. The modelling and computational simulation of vertebroplasty, i.e., bone-cement-injection into the vertebra, is of major interest to obtain valid and reliable predicitions for this surgery. A detailed micromechanical (and locally single-phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts and their complex microstructure have to be known. Therefore, this study considers a macro-scopic (and multi-constituent) continuum-mechanical model based on the Theory of Porous Media, where the homogenisation of the underlying micro-structure results in a model of three constituents. In particular, these are the solid bone skeleton, which is saturated by bone marrow, where the latter may be displaced by the injected liquid bone cement. The micro-architecture is regarded by heterogeneous and anisotropic permeability tensors and the preferred directions of the trabecular bone structure. The presented strongly coupled macroscopic model offers the opportunity to not only simulate the flow of the pore fluids but also predicts the arising stresses and strains of the solid bone skeleton due to the numerical investigation of the injection process. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticity of the governing field equations. A possible approach to solve these problems is to introduce a non-local field function in the model which includes an internal material length scale. For this purpose a gradient-enhanced free energy function is used for the current continuum damage model from which two variational equations are resulting. Calculations with less effort can be achieved due to the enhancement of the free energy function in comparison to other approaches. The mentioned model is applied to a material with locally varying damage properties (yield limits). Furthermore, the model is able to describe crack propagation in cases of completely damaged material. Therewith, a matrix material including precipitates, such as carbides, is modeled. This allows to investigate ship screws, which usually exhibit the mentioned composition, with regard to the influence of cavitation. Cavitation describes the implosion of risen vapor bubbles, whereby the impact on screws causes heavy damages which can lead to a complete destruction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For a reliable prediction of crack paths, on the one hand the accurate calculation of crack tip loading quantities is inevitable, on the other hand orthotropic features of the fracture toughness need to be taken into account. The interplay of crack tip loading and material response due to fracture is still unclear and seems to have a crucial effect on crack path predictions. Numerical tools for the accurate calculation of crack tip loading quantities using path-invariant J-integrals and interaction integrals (I-integral) are presented. Here, global approaches are beneficial when considering crack tips approaching other crack faces or internal boundaries. Curved crack faces have to be taken into account and special treatment regarding crack face integrals is necessary. Experimental investigations are carried out at standard CT-specimens of rolled aluminum alloy Al-7075 exhibiting a directional orthotropy of the fracture toughness. Considering that property, the numerically predicted crack paths based on FE calculations show very good agreement with subcritically grown paths obtained from experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Due to the different coefficients of thermal expansion of aluminium and silicon, high residual stresses of second order occur in Al-Si alloys depending on the cooling rate during the molding process. In products as for example crank cases made of Al-Si alloys these residual stresses may cause microcracks. In the work at hand measurements of the eigenstresses in the single phases (i.e. residual stresses of second kind) performed via neutron diffractometry are compared to numerical simulations for a specific cooling rate. To this end a three-phase model is presented, which considers the α aluminium, the eutectic aluminium, and the silicon particles. The presented model is able to predict the residual stresses in the single phases within an elastoplastic framework. The simulation of tensile loadings of these structures are compared to experiments. The numerical computations are carried on stochastic geometry models by using a fast solver [1] for the Lippmann-Schwinger integral equation, which is based on the fast Fourier transformation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the effect of different stress states on plastic deformations, damage and fracture of ductile materials. To be able to model these effects a continuum damage model has been introduced taking into account the dependence of stress-state on the constitutive equations. The model is based on the introduction of damaged and fictitious undamaged configurations. All parameters appearing in the constitutive equations are stress-state-dependent which can be characterized by the stress intensity, the stress triaxiality and the Lode parameter. Only experiments are not adequate enough to determine all constitutive parameters. Thus, additional series of 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 stress triaxialities and Lode parameters in tension, shear and compression domains. After all, the results from the micro-mechanical simulations are used to suggest the damage equations and to identify corresponding parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper deals with the modeling of fiber-reinforced PMMA. Focus is on the macroscopic mechanical response with emphasis on the fracture properties such as the ultimate strength and the fracture energy. In order to capture the macroscopic mechanical response of PMMA, a finite element formulation is presented. While the elastic response of the fibres and that of the surrounding matrix are modelled in standard manner, i.e., by standard bulk material models, the relevant failure modes such as cracking of the fibres are accounted for by means of the so-called Strong Discontinuity Approach (SDA). Since the fibres are relatively small, their fracture mechanical properties crucially depend on their geometry, i.e., they show a pronounced size effect. Based on numerical analyses of fibres with different geometries, the aforementioned size effect is naturally incorporated into the formulation [1]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The lifetime of structural components is limited by fatigue cracks. After initiation from an existing defect the crack grows subcritically until it reaches a critical size. At this point it becomes unstable and the structural component fails. PROCRACK is a powerful tool that enables the commercial finite element software Abaqus to calculate the crack propagation in pre-cracked components. The complete capability of Abaqus can be used to simulate nearly arbitrary geometries. Abaqus/CAE is used for the three-dimensional modeling of the initial crack at a geometrical level by means of points, lines and triangles. The numerical analysis is performed by Abaqus/Standard. PROCRACK automatically generates a tube-shaped submodel around the crack front to calculate the stress intensity factors with high accuracy. The Paris law or the NASGRO equation can be used to calculate the incremental crack growth. The shape of the crack and the finite element mesh are updated in every crack growth step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution presents ideas, how crack propagation in three-dimensional solids composed of anisotropic materials can be predicted using the Griffith energy principle. Since the work of Irwin the change of potential energy caused by a straight elongation of a crack in an isotropic two-dimensional homogeneous structure can be expressed in quadratic terms of the stress intensities at the crack tip. This result was generalized in the last decades using methods of asymptotic analysis by many authors [1] to more complicated geometries, to anisotropic and inhomogeneous materials. With the energy release rate at hand, quasi-static scenarios of crack propagation can be simulated for plane problems [2], but this is still a complicated task for three-dimensional problems [3]. We show an idea how the change of energy caused by propagation of a crack surface in a fully three-dimensional solid of nearly arbitrary shape can be computed in anisotropic materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A simple and concise mathematical model describing the deformation and the electrical behavior of a bi-morph piezoelectric curved sensor subjected to pure bending is developed. In particular, the influence of the couple moment on the electrical potential generated in the sensor is investigated and the results are presented in graphical form. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Although machining is a well established method in manufacturing, the numerical modeling is complicated since severe changes in the geometry and the topology can occur. Especially the formation of chips and burrs requires a method that tracks the large configurational changes. The particle finite element method (PFEM) combines the benefits of the standard finite element method (FEM) and discrete models, such as molecular dynamics simulations and is therefore well suited to cope with these tasks. In this article, a description of the conceptual realisation and the overall algorithm is given and a numerical analysis of a cutting process is performed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The scaled boundary finite element method (SBFEM) has been used in many fields of engineering to solve the governing equations in bounded and unbounded 2D as well as 3D domains. In solid mechanics, the semi-analytical solution strategy of the SBFE formulation (numerical in circumferential direction, analytical in radial direction) is based on the assumption of linear elastic material behavior and only small geometrical changes. However, a large group of materials (e.g. rubber) shows geometrical and physical nonlinearity at mechanical loading. In this contribution, the extension of the SBFEM to geometrical and physical nonlinearity is examined. A plane finite element is developed which uses the concept of shape functions constructed by the SBFEM in the framework of a nonlinear finite element analysis. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Volume 14 (2014) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 85th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, held 10 – 14 March 2014 at Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections Minisymposia M 1 Control of Differential-Algebraic Equations M 2 Parametric Model Reduction of Dynamical Systems M 3 Generalized Finite Elements Sections 1–24 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 image processing 22 Scientific computing 23 Applied operator theory 23 Young Researchers' Minisymposia YR 1 Multiscale Geometric Image Analysis YR 2 Geometry and Shape Optimization YR 3 Time-parallel Methods YR 4 Recent Advances in Porous Metal Plasticity YR 5 Variational Models in Elasticity and Plasticity

Description: Comprehension and correct interpretation of EMG signals and their generation could still be well improved. Computational models that can predict the EMG signal resulting from realistic motor unit recruitment as well as the underlying biophysical processes of single skeletal muscle fibres are therefore highly desirable. Having such a model available, one can test, verify and improve algorithms determining motor unit recruitment. Here, we present a three-dimensional, continuum-based, forward model that is able to produce a virtual EMG signal based on the underlying biophysical principles of skeletal muscle fibre activation. The result is a virtual EMG signal for complex and realistic geometries that may even undergo deformations as in the case of dynamic contractions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Al/Mg compounds produced by hydrostatic extrusion exhibit unique characteristics regarding high strength and low weight, which are required by safety part applications in lightweight constructions. Between the two materials an interface in form of a brittle intermetallic phase consisting of Al 2 Mg 3 and Al 12 Mg 17 arises during the production process. However, a certain plastic deformability of the semi-finished product is essential for further forming processes. Even under multi-axle load during a radial upsetting process, the interface maintains a full material joint although a fragmentation and a new secondary interface between the fragments can be observed. Due to the evaluations of light microscopy images and Eulerian Hencky strain values at the interface, which are obtained with the help of the Digital Image Correlation, a relation between the strain and the boundary layer's appearance seems reasonable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Configurational forces can be interpreted as driving forces on material inhomogeneities such as crack tips. In dissipative media the total configurational force on an inhomogeneity consists of an elastic contribution and a contribution due to the dissipative processes in the material. For the computation of discrete configurational forces acting at the nodes of a finite element mesh, the elastic and dissipative contributions must be evaluated at integration point level. While the evaluation of the elastic contribution is straightforward, the evaluation of the dissipative part is faced with certain difficulties. This is because gradients of internal variables are necessary in order to compute the dissipative part of the configurational force. For the sake of efficiency, these internal variables are usually treated as local history data at integration point level in finite element (FE) implementations. Thus, the history data needs to be projected to the nodes of the FE mesh in order to compute the gradients by means of shape function interpolations of nodal data as it is standard practice. However, this is a rather cumbersome method which does not easily integrate into standard finite element frameworks. An alternative approach which facilitates the computation of gradients of local history data is investigated in this work. This approach is based on the definition of subelements within the elements of the FE mesh and allows for a straightforward integration of the configurational force computation into standard finite element software. The suitability and the numerical accuracy of different projection approaches and the subelement technique are discussed and analyzed exemplarily within the context of a crystal plasticity model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The microplane model allows for the description of damage induced anisotropy in a natural manner by introducing constitutive laws for quantities on individual microplanes at each material point. However, if damage or other strain softening constitutive laws are used within the microplane approach, the well-known problem of localization arises leading to pathological mesh dependency. This contribution focuses on the implicit gradient enhancement and its efficient application to regularize microplane damage models. Previous works enhanced the strain tensor, thus resulting in large number of additional degrees of freedom. A new method which enhances the equivalent strain driving the damage on each microplane is introduced. The new method limits the number of additional degrees of freedom to one, while preserving the regularizing effect. The capabilities of the proposed formulation are demonstrated by a numerical example. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Structural damage detection using vibration response signals is appealing in recent years since it does not require the identification of the modal parameters or building the structures' finite element model, among which the correlation-function-based damage detection methodologies is a novel topic [1]. Beginning with the introduction of the correlation function theory, this paper proposes a new damage detection strategy using the auto correlation function values of vibration response signals of the structure. The maximum value of the auto correlation functions of the vibration responses from different measurement points are used to form the damage index to locate the damage. Differences of the damage index are used to make the damage location more clearly. As in real world applications, structures may undergo different external excitations [2]. Different external excitations are input into the intact and damaged structure. The results from numerical simulation of stiffness reduction detection of a 12-story frame structure show that the proposed strategy can locate the damage correctly and has a very good anti-noise ability under inconsistent external excitations. As only the vibration responses before and after damage are used in this damage detection strategy, it can be a useful tool for structural health monitoring. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: To compare measured and calculated mode shapes, the natural frequencies and the mode shapes must be checked. For sensitivity analysis, which is the first step when optimizing parameters, the results must be automatically evaluated. When evaluating mode shapes and dependent natural frequencies, numerical values have to be determined. In this paper, a method is shown, how mode shapes and natural frequencies can be considered within one value for each mode shape. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Oil service companies use highly complex drill string models to optimize drilling assemblies and to perform post-drilling analysis. These drill string models are usually non-linear, FEM based and able to describe arbitrary curved well bore geometries. One of the most critical parts is the description of the contact at the well bore wall. Due to the model's complexity, simulations in time domain are extremely expensive and can take days to weeks. Less results in the same time reduce the quality of optimization and parameter studies. Thus, one goal of research is to accelerate time domain simulations while maintaining an appropriate level of accuracy. One way to reduce simulation time is to lower the order of the system. There are a lot of common well-developed order-reduction-techniques for linear-systems, e.g., modal reduction. However, these methods cannot handle unilateral-constraints as used for the wall contact description. Hence, a reduction technique for non-linear systems is needed. A promising reduction method of this kind is the proper orthogonal decomposition (POD, also called Karhunen-Loève Transformation). This technique determines the principal structure of motions based on time signal measurements. The system is then reduced by transforming it to a lower dimensional space build on these main structures. In this paper the POD will be applied to a basic drill string model. It is a 2D-FEM beam-element drill string system with linear penalty-springs. Parameter studies of the contact stiffness and the degree of reduction will show the performance and possible gain of this reduction method. Finally advantages and inconveniences of this method for drill string dynamics will be discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For nonlinear transient problems as well as rather slow quasi-static processes explicit time integration has proven to be a suitable and robust time integration algorithm. As a consequence of the Courant-Friedrichs-Lewy (CFL) criterion small time step sizes are necessary and the overall computation time is dominated by the operations on element level. Privileged use of low order finite elements is common in explicit time integration due to their efficiency and robustness. In order to suppress artificial locking effects the work of Bischoff and Romero [1] is followed where a generalization of the method of incompatible modes (IM) is derived being equivalent to the class of enhanced assumed strain (EAS) elements originally proposed by Simo and Rifai [2]. These concepts are bound to a static elimination procedure of internal parameters which may result in a considerable expansion of the computational costs in the case of an explicit time integration scheme. In order to avoid the static elimination procedure inertia is considered for the incompatible parameters as suggested by Mattern et al. [3, 4]. This step allows integrating the incompatible parameters directly in time, but since rather large stiffnesses are related to the incompatible parameters – particularly for the volumetric mode enhancements – the highest eigenfrequency may be increased which would lead to a decrease of the time step size. This motivates scaling the masses associated to these incompatible parameters to control their effect on the time step size. It is possible to derive analytically based estimates for the scaling of the IM-masses in order to achieve results agreeing very good with the classical EAS approach including large deflections and nonlinear material behaviour with elasto-plasticity. The numerical implementation is performed using AceGen [5]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Elastic stress state of a thick-walled cylindrical panel, which is subjected to a positive temperature gradient in the radial direction, is investigated under generalized plane strain conditions. In particular, the stress distributions in the panel at the elastic limit according to von Mises' yield criterion are studied. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Contact between arbitrary curved ropes and arbitrary curved rough orthotropic surfaces has been revised from the geometrical point of view. Variational equations for the equilibrium of ropes on orthotropic rough surfaces are derived, first, using the consistent variational inclusion of frictional contact constraints via Karush-Kuhn-Tucker conditions expressed in Darboux basis. Then, the systems of differential equations are derived for both statics and dynamics of ropes on a rough surface depending on the sticking-sliding condition for orthotropic Coulomb's friction. Three criteria are found to be fulfilled during the static equilibrium of a rope on a rough surface: “no separation”, condition for dragging coefficient of friction and inequality for tangential forces at the end of the rope. The limit tangential loads still preserve the famous “Euler view” T = T 0 e ω s for the curves and surfaces of constant curvature. It is shown that the curve of the maximum tension of a rough orthotropic surface is geodesic. Equations of motion are derived in the case if the sliding criteria is fulfilled and there is “no separation”. Various cases possessing analytical solutions of the derived system, including Euler case and a spiral rope on a cylinder are shown as examples of application of the derived theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Computational resources can be used more efficiently by introducing reduced-order models, instead of solving large systems of equations of the original model. In this contribution, the Krylov subspace method, a reduced-order modeling method, is studied and compared to the modal decomposition for a rubber wheel model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: To model the contact behavior including dynamical effects, a two dimensional mechanical model of elastic rough contact is developed. This model can simulate the contact behaviour between two rough surfaces depending on normal pressure, sliding speed and roughness profiles. The contact between two rough surfaces is reduced to a rough rigid and a rough elastic layer. The elastic layer is modeled by point masses connected by spring-damper elements. The total system is described by coupled ODEs. The number of ODEs and thus the degree of freedom of the model depends on the varying contact conditions. The contact conditions are monitored during the simulation and the simulation interrupts, in case the contact conditions change. The equations of motion are then adapted with respect to the contact constraints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present work deals with the solution of geometrically nonlinear elastic problems solved by the least-squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower-order elements. Basis for the mixed element is a first-order stress-displacement formulation resulting from a classical least-squares method. Similar to the ideas in SCHWARZ ET AL. [1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least-squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The aim of this paper is to present the available modeling strategy available for description of the packaging behavior, which often takes place in the foams. The packaging process is modeled by means of approaches, which are used in the phase transformation theory. The constitutive model is based on the double-well elastic potential, which is defined for small strains. Two principal approaches are used for the research: discrete method based on the Voronoi tessellation and phase-field method. Discrete modeling approach is required for the estimations of the critical stresses in foams, which leads to the initiation of the packaging process. The phase-field approach is the continual approach, which is required for description of the packaging propagation in the foam. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present work a mixed finite element based on a least-squares formulation is proposed. In detail, the provided constitutive relation is based on a hyperelastic free energy including terms describing a transversely isotropic material behavior. Basis for the element formulation is a weak form resulting from a least-squares method, see e.g. [1]. The L 2 -norm minimization of the residuals of the given first-order system of differential equations leads to a functional depending on displacements and stresses. The interpolation of the unknowns is executed using different approximation spaces for the stresses ( W q (div, Ω)) and the displacements ( W 1,p (Ω)), under consideration of suitable p and q . For the approximation of the stresses vector-valued shape functions of Raviart-Thomas type, related to the edges of the respective triangular element, are applied. Standard interpolation polynomials are used for the continuous approximation of the displacements. The performance of the proposed formulation will be investigated considering a numerical example. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In Finite Element Analysis (FEA) the discretisation has wide influence on the quality of the analysis. With r-adaptive FEA it is aimed to improve the finite element solution by finding the optimal mesh without changing the mesh connectivity and the order of the elements. Thus, this approach belongs to the group of mesh-moving methods. The r-adaptivity approach presented is governed by energy minimisation and therefore is called energy-based. It is built upon a variational Arbitrary Lagrangian-Eulerian (vALE) formulation whereby the potential energy is varied with respect to spatial and material coordinates. However, even for simple problems the Hessian is likely to be singular or indefinite. This complicates the application of solution schemes based on Newton's method. Motivated by the approaches of [1–4], we try to find appropriate numeric methods for r-adaptivity. For this purpose, we study the numerical performance of a primal barrier scheme, of an augmented Lagrange barrier scheme and the primal-dual interior point package IPOPT. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We investigate the coupling of the four one-dimensional problems of linear elasticity (i.e., the rod-, the two beam- and the shaft-problem), for the case of a cross section that has two orthogonal axes of reflectional symmetry. An analytical proof is given, that the problems are decoupled for a homogeneous orthotropic material and the coupling behavior is given for monoclinic materials in dependence of the orientation of the symmetry plane. For a general anisotropic (aelotropic) material all four problems are coupled. We also identify the driving forces for the four problems, leading to a detailed definition of the admissible load-cases for the classical problems, so that any three-dimensional load-case can be uniquely decomposed into the driving forces of the four problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this work, an approach for computing three-dimensional structures with random material properties, such as the yield stress, Young's modulus and hardening parameters is proposed. The random material properties are represented as random fields which are realized with the Spectral Representation Method (SPRM). The proposed approach is coupled with Monte Carlo Simulation (MCS) to determine the response statistics of a simple mechanical structure. The numerical results are compared with those obtained from classical Latin Hypercube Sampling (LHS). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We investigate a model of dynamic recrystallization in polycrystalline materials. A probability distribution function is introduced to characterize the state of individual grains by grain size and dislocation density. Specifying free energy and dissipation within the polycrystalline aggregate we are able to derive an evolution equation for the probability density function via a thermodynamic extremum principle. Once the distribution function is known macroscopic quantities like average strain and stress can be calculated. For distribution functions which are constant in time, describing a state of dynamic equilibrium, we obtain a partial differential equation in parameter space which we solve using a marching algorithm. Numerical results are presented and their physical interpretation is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Co-simulation is a simulation technique for time dependent coupled problems in engineering that restricts the data exchange between subsystems to discrete communication points in time. In the present paper we follow the block-oriented framework in the recently established industrial interface standard FMI for Model Exchange and Co-Simulation v2.0 and study local and global error of co-simulation algorithms for systems with force-displacement coupling. A rather general convergence result for the co-simulation of coupled systems without algebraic loops shows zero-stability of co-simulation algorithms with force-displacement coupling and proves that order reduction of local errors does not affect the order of global errors. The theoretical investigations are illustrated by numerical tests in the novel FMI-compatible co-simulation environment SNiMoWrapper . (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Variational integrators are modern time-integration schemes based on a discretization of the underlying variational principle. They thus skip the direct formulation and time discretization of partial differential equations. In mechanics, Hamilton's Principle is approximated by an action sum whose variation should be equal to zero, resulting in discrete Euler-Lagrange Equations or equivalently in discrete Position-Momentum Equations. Variational integrators are, by design, structure preserving (symplecticity) and show excellent long-time behavior. In order to consider the coupling between mechanical and thermal quantities, Hamilton's principle is extended by using the notion of thermacy as thermal analogue to mechanical displacements. From this variational formulation, a variational integrator using the generalized trapezoidal rule is constructed exemplarily. A thermoelastic double pendulum with heat conduction serves as a model problem. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents a dynamic programming approach for calculating time optimal trajectories for industrial robots, subject to various physical constraints. In addition to path velocity, motor torque, joint velocity and acceleration constraints, the present contribution also shows how to deal with torque derivative and joint jerk limitations. First a Cartesian path for the endeffector is defined by splines using Bernstein polynomials as basis functions and is parameterized via a scalar path parameter. In order to compute the belonging quantities in configuration space, inverse kinematics is solved numerically. Using this and in combination with the dynamical model, joint torques as well as their derivatives can be constrained. For that purpose the equations of motion are calculated with the help of the Projection Equation. As a consequence of the used optimization problem formulation, the dynamical model as well as the restrictions have to be transformed to path parameter space. Due to the additional consideration of jerk and torque derivative constraints, the phase plane is expanded to a phase space. The parameterized restrictions lead to feasible regions in this space, in which the optimal solution is sought. Result of the optimization is the time behavior of the path parameter and subsequently the feed forward torques for the optimal motion on the spatial path defined by previously mentioned splines. Simulation results as well as experimental results for a three axes industrial robot are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A method to optimize energy efficiency for bipedal running robots is presented. A running model of a simple bipedal robot consisting of five rigid bodies connected by actuated revolute joints is introduced. The actuators' torques are generated by a trajectory tracking controller to produce periodic running gaits. The controller's reference trajectories are parameterized by Bézier polynomials. A numerical optimization is used to employ reference trajectories with optimal energy efficiency for average velocities in the range of 1.5 to 5.5 m/s. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A modular modelling strategy which combines motion equations in generalized coordinates with those formulated in terms of redundant coordinates is presented. The general idea is illustrated by the planar model of a multiple pendulum in the gravitational field whose upper end is spatially fixed, while its lower end is attached to an elastically guided box. It is shown how the governing differential-algebraic system of equations can be reduced to a system of linear differential equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The lateral motion of vehicles on tracks and roads is characterized by the rolling contact between wheels and guideway. Railway vehicles feature passive lateral guidance while road vehicles are operated by steering. Lateral dynamics is an extremely complex problem but the fundamental behaviour can already understood by strongly simplified mechanical models. In this paper the historical development of modelling approaches for lateral dynamics is reviewed what is very helpful for benchmarking and checking more complex problems, too. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution, a methodology for the calculation of optimal bounds on the probability of failure of soft biological tissues is presented. Two potential rupture criteria are considered and an uncertainty quantification method [1] is applied to a virtual experimental data set. The results for both criteria are compared in a finite element example. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Biomechanical investigations of human cartilage, especially intervertebral discs (IVDs), have greatly helped to improve people's health over the last several decades. The study of the underlying biomechanical characteristics of cartilage tissues is a key issue to understand its physiological function and degeneration or damage behavior. The aim of this investigation is to describe the biomechnical behavior of healthy sheep IVDs under various loading conditions. Experimental and cartilage histological data, including fiber orientation, are used to develop a viscohyperelastic material model, which allowed us to numerically study the mechanical behavior of IVDs, consisting of a cartilaginous, fiber-reinforced ring surrounding a highly hydrated, gelatinous core. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Industry as well as the private domain show an increasing interest to the field of mobile robotics. With a higher number of applications, the complexity of the required tasks rises, and therefore the community tends to use robots with many degrees of freedom (DOF). The present paper takes this topic up and focuses on challenges of the kinematical modeling of redundant, non-holonomic mobile robots by considering a 12 DOF platform. To reach an omnidirectional behaviour, the actuated wheels are diagonally mounted on the chassis. Well known problems resulting from this set-up are parametric singularities which unnecessarily restrict the motion of the mathematical model. As it turns out, this problem can be avoided by the use of a non-minimal parametrized model. An additional challenge results from the inverse kinematic (IK) problem on velocity level. The corresponding equations are highly underdetermined and, due to the non-holonomic wheels, not directly affected by the steering angle velocities. This problem is solved by performing a local optimization on acceleration level. Finally, simulation results are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Under supra-physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro-mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Fatty liver is a common disease in the western society. Different stimuli, such as obesity or abuse of alcohol, cause the liver to store fat within liver cells, the so called hepatocytes. This growth induced by storage of fat influences the perfusion of the overlying structures, i. e. sinusoids, liver lobules, liver lobes, and consequently the liver itself. The scales of these structures reach from few µm (size of a hepatocyte) to several cm (size of liver). In view of finite element (FE) simulations, the necessity of introducing different scales becomes obvious. For the description of growth effects in the liver the relevant quantities are: perfusion of the liver and amount of substances that are needed for production of fat (glycogen and fatty acids). In this work we present a multiphasic continuum mechanical model for the description of micro-perfusion in the liver lobule using a homogenized multiphasic approach based on the theory of porous media (TPM). Into this model we inserted a zero-dimensional (0D) kinetic model calculating rates of all relevant substances. So far, the model focuses on the time dependent and spatial zonation of glycogen, since production of fat heavily depends on the stored glycogen. Additionally, a possible method for incorporating fatty acids and therefor also growth will be presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In biomedical engineering, it is a common practice to replace injured cartilage by implants, which are seeded with human cartilage cells. Before implanting, the implants are cultivated and usually stimulated electrically or mechanically in a bioreactor to initiate cell multiplication and oriented cell growth. A new experimental set-up is developed leading to the possibility of stimulating such implants in a multi-dimensional, physiologically consistent way. In cooperation with the University Medical Centre Aachen, a human knee simulator is developed. Cell-seeded implants are placed in a recreated human environment and stimulated with several load cycles of reproduced walking. After the cultivation period, the implanted material is removed and biologically and mechanically evaluated. The quality of the implanted material as well as the influence of the body-conformable load on the material is studied. To understand the correlation between tissue remodelling and mechanical load history, the load and movement scenario is also numerically investigated. For this reason, the experiment is transferred to a geometrically realistic FE model of a human knee. As a first approach, an elastic material model is used. The aim is to have a predictive FE model with an optimal trade-off between accuracy and efficiency using an appropriate material formulation. The results will be compared to experimental data. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A collagen foil, which plays an important role for cultivating and investigating tendon cells, is investigated experimentally and numerically: The foil, which should later serve as a scaffold for tendon cells in a custom made bioreactor, is stimulated periodically in an in situ experiment. Additionally, a material model to describe the anisotropic structure and the relaxation behaviour of the collagen foil is used to simulate the material response. By comparing the measurements and simulations, the stress and strain states in the foil can be determined. Hence, the material parameters for the presented experimental set up are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Modeling of complex mechanisms leading to the functioning of the heart has been an active field of research since decades. Difficulties associated with in vivo experiments motivate the utilization of computational models in order to gain a better appreciation of heart electromechanics. Although rate dependent behaviour of the orthotropic passive heart tissue has been comprehensively studied in the literature [1], effects of this phenomenon on fully coupled cardiac electromechanics are unrevealed yet. Therefore, this contribution is concerned with the investigation of viscous effects on the electromechanical response of the myocardium. To this end, we adopt the fully implicit finite element framework which strongly couples the mechanical and electrophysiological problem of the myocardium in a mono- and bi-domain setting [2,3], respectively. Viscous effects, however, are consistently embedded into this framework by making use of the orthotropic viscoelastic material model for the passive myocardium, which considers different relaxation mechanisms for the different orientation directions [5]. The performance of the proposed model is assessed by comparing finite element simulations of spiral waves in heart tissue for elastic and viscoelastic formulations. We further investigate the influence of viscosity on the defibrillation phenomenon by means of the finite element formulation of bidomain electrophysiology. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Serious diseases within the brain's tissue often require a medical intervention, such as the treatment of brain tumours. The present contribution aims at predicting the expected impacts of a scheduled clinical procedure via numerical simulations based on a sophisticated constitutive model. The enormous complexity of the tissue's microscopic composition encourages the application of the Theory of Porous Media (TPM), providing a well-suited way to model the brain's tissue aggregate in a compact manner on the macroscale. In particular, a multi-component model is used which is strongly related to the drug-delivery problem within the brain's tissue, cf. [2]. In this model, the solid skeleton is given by the tissue cells (with cell content) and the vascular walls. This solid skeleton is perfused by two mobile but basically separated pore-liquid constituents, the blood and the overall interstitial fluid constituent. To provide the particular description of administered therapeutic agents within the overall interstitial fluid, this real mixture is treated as a chemical solution of two components. These are the liquid solvent and the dissolved therapeutic agent (drug). Numerical examples demonstrate the applicability of the derived model. In particular, infusions of therapeutics into the extra-cellular space (ECS) are simulated under various conditions and complemented by an evaluation of the local numerical sensitivity to survey the influence of certain involved parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: [EN] In this work, a nonlocal damage model is proposed for dynamic analysis of viscoplastic shell structures using the phase-field approach. A phase-field variable on the mid surface is introduced to characterize the nonlocal damage as well as the transition between undamaged and damaged phase. The total free energy in [1] is modified as a sum of Helmholtz free-energy and Ginzburg-Landau one. The latter is defined as a function of the phase-field variable and its corresponding gradient. This enhancement gives rise to an introduction of gradient parameters in terms of a substructure-related intrinsic length-scale. The evolution of the phase-field based damage variable can be found from the minimum principle of the dissipation potential [3]. The performance of the proposed model is demonstrated through numerical results of a plate with a circular hole. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Recently developed continuum phase field models for brittle fracture show excellent modeling capability in situations with complex crack topologies including branching in the small and large strain applications. This work presents a generalization towards fully coupled multi-physics problems at large strains. A modular concept is outlined for the linking of the diffusive crack modeling with complex multi field material response, where the focus is put on the model problem of finite thermo-elasticity. This concerns a generalization of crack driving forces from the energetic definitions towards stress-based criteria, the constitutive modeling of degradation of non-mechanical fluxes on generated crack faces. Particular assumptions are made on the generation of convective heat exchanges approximating surface load integrals of the sharp crack approach by distinct volume integrals. The coupling effect is also shown in generation of cracks due to thermally induced stress states. We finally demonstrate the performance of the phase field formulation of fracture at large strains by means of representative numerical examples. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This paper presents a multi-level model for the description of hydraulic effects of fracture within the context of Enhanced Geothermal Systems. The standard Biot's poroelastic formulation is used to model the physical processes in a geomechanical reservoir in terms of the material deformation and the fluid pressure. Crack propagation is modeled using the phase field method. The influence of a propagating fracture on permeability is taken into account by using a micromechanical homogenization technique. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Ultra High Performance Concrete (UHPC) is defined as a new generation of concrete which shows improved performance and higher strength than traditional concrete. This allows to realize slender and much more durable structures and in this way significantly reduces the required resources. Despite its huge potential in construction, technical information about this new type of material is still limited. This contribution presents investigations on the dynamic mechanical behavior and properties of UHPC specimens by spalling experiments. Two different recipes were used to compare the properties. Due to the special specimen geometry (slender cylindrical) a flowable consistency was required to enable a sufficient degassing of the mixtures. For the test, a Split Hopkinson Pressure Bar (SHPB) has been modified and used. A high speed photograph system was focused on the fragmentation process during the test. On the basis of these experiments the dynamic E-moduli as well as the dynamic tensile strength of the UHPC specimens were determined. By observation of the specific crack patterns on each tested specimen and corresponding times, the dynamic fracture energy is calculated. Numerical simulations also were performed and compared to the experimental result. It is concluded that the dynamic tensile strength of the UHPC increases at higher strain rates. The results of the current study provide technical information about fracture and dynamic behavior of UHPC and the obtained values could be used for future computational models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present work investigates a reliable method of integrating the evolution equations of constitutive models for amorphous thermoplastics that typically utilize a power-law or exponential-type flow rule. When it comes to sudden changes in the external stress (e.g. element deletion technique in explicit finite element analysis) these functional dependencies need a special treatment to assure a numerically stable integration of the evolution equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The numerical modeling of failure mechanisms due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by recently developed diffusive crack modeling concepts, which are based on the introduction of a crack phase field. Such an approach is conceptually in line with gradient-extended continuum damage models which include internal length scales. In this paper, we extend our recently outlined mechanical framework [1–3] towards the phase field modeling of fracture in the coupled problem of fluid transport in deforming porous media. Here, extremely complex crack patterns may occur due to drying or hydraulic induced fracture, the so called fracking. We develop new variational potentials for Biot-type fluid transport in porous media at finite deformations coupled with phase field fracture. It is shown, that this complex coupled multi-field problem is related to an intrinsic mixed variational principle for the evolution problem. This principle determines the rates of deformation, fracture phase field and fluid content along with the fluid potential. We develop a robust computational implementation of the coupled problem based on the potentials mentioned above and demonstrate its performance by the numerical simulation of complex fracture patterns. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Regeneratively cooled nozzle structures of Reusable Launch Vehicles (RLV) belong to the most critical components of a space shuttle main engine. The so-called doghouse effect is a failure mode in the rocket combustion chamber wall, which has been observed experimentally. Within the Collaborative Research Centre SFB-TR 40 of the German Research Foundation (DFG), new technologies for the future space-transport-systems are being developed. By using a new continuum mechanical approach, motivated by a rheological model, we are able to reproduce the doghouse effect. Moreover we intend to give reliable lifetime predictions for rocket combustion chamber structures so that in future components can be tested virtually instead of conducting real experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the effect of stress state on damage and failure behavior of isotropic ductile metals. In the continuum damage model the damage behavior of ductile metals is adequately described by a generalized damage condition and an anisotropic damage rule. The damage criterion is based on series of uniaxial experiments with differently notched specimens and corresponding numerical simulations as well as on various numerical calculations on the micro-scale. Different branches of the damage criterion depending on stress triaxiality and Lode parameter are considered. To be able to validate the proposed stress-state-dependent functions new experiments with two-dimensionally loaded specimens have been developed. Corresponding numerical simulations show that these shear-tension and shear-compression tests cover a wide range of stress triaxialities and Lode parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate- and temperature-dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro-mechanical numerical simulations of void containing unit-cells. In this context results of dynamic micro-mechanical simulations are presented which can be used to study the damage effects on the micro-scale and to validate the rate-dependent continuum damage model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Three-dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi-analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter-fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three-dimensional crack configurations in composite laminates so-called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A microstructural simulation model is proposed which accounts for damage accumulation in shear bands and deformation-induced martensite formation in a metastable austenitic stainless steel (AISI304). The model is numerically solved using the two-dimensional (2-D) boundary element method. By using this method, sliding displacements can be directly evaluated in shear bands and austenite grains as well as generated martensite domains with their individual mechanical properties and shape deformation can be considered. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The assumption of purely local continuum damage formulations may imply a loss of well-posedness of the underlying boundary value problem. With regard to numerical methods such as the finite element method, this may lead to mesh-dependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, i.e. to regularise the problem, we, in this contribution, apply a non-local gradient-based damage formulation within a geometrically non-linear setting allowing for large deformations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The lifetime of adhesively bonded joints under service loading is predicted by a linear viscoelastic traction–separation model, which is enhanced by an isotropic damage approach. Therefore, a scalar damage variable is defined according to the concept of effective stresses based on the hypothesis of strain equivalence in the framework of continuum damage mechanics. The damage evolution is driven by a specific equivalent stress, adapted for ductile adhesives. Experimental data acknowledge the validity of the proposed model for the lifetime prediction of adhesive joints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)