ALBERT

Description: A Fluid–Structure Interaction (FSI) problem can be reinterpreted as a heterogeneous problem with two subdomains. It is possible to describe the coupled problem at the interface between the fluid and the structure, yielding a nonlinear Steklov–Poincaré problem. The linear system can be linearized by Newton iterations on the interface and the resulting linear problem can be solved by the preconditioned GMRES method. In this work we investigate the behavior of preconditioners of Neumann–Neumann and Dirichlet–Neumann type. We find that, in the context of hemodynamics, the Dirichlet– Neumann, i.e., using Dirichlet boundary conditions on the fluid side and Neumann on the structure side, outperforms the Neumann–Neumann method, except when a weighting is used such that it basically reduces to the Dirichlet–Neumann method. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An algorithmic strategy for the modelling and simulation of bone healing is presented. The algorithm works directly on the computed tomography data and simulates, after an appropriate volume meshing, a mechainically driven healing concept which is based on competitive and dynamical mechanical parameters. The finite element simulations are done with realistic boundary conditions from patient-specific OpenSim simulations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the current contribution, we present a multi-scale constitutive model capturing macroscopic inelastic effects (like stress softening and permanent set) in soft tissues under cyclic loading. Soft biological tissues can be described as a biological composite material. The extracellular matrix is hereby reinforced by collagen fibers which themself are an assembly of collagen fibrils embedded in a proteoglycan (PG) rich matrix. Micro-damage induced by cyclic loading is treated by an interaction scenario between the fibrils and the PGs. At the low strain regime PGs promote sliding between fibrils [1] which leads to the yielding of statistical distributed overlapping segments. The breakage of the PG-bridges is defined by a decreasing PG-density. Due to the accumulated damage of the PG connections at high tissue strains, the strains at the fibril level increases. This finally drives the over-stretching of the fibrils, which is associated with a permanent rupture of the hydrogen bonds inside of the tropocollagen molecules [2]. The so obtained model is in line with recent experimental findings [1, 2] and was additionally validated against experimental data available in literature. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We present an application of the phase-field method of fracture to the simulation of artery rupture at large strains. To achieve this, the crack driving force function associated with the evolution of the crack phase-field is modified to account for the inherent anisotropy of the soft biological tissues. The phase-field methods present a promising and innovative approach to the thermodynamically consistent modeling of fracture. A key advantage lies in the prediction of the complex crack topologies where the cohesive zone approaches to fracture are known to suffer. A regularized crack surface functional is introduced that Γ-converges to a sharp crack topology for vanishing length scale parameter. The evaluation of the phase-field follows the minimization of this crack surface functional. The phase-field variable can be treated as a geometric quantity whose evolution is coupled to the anisotropic bulk response in a modular format in terms of a crack driving state function. A stress-based anisotropic failure criterion is introduced whose maximum value from the deformation history drives the irreversible crack phase-field. The formulation is verified by the finite element based simulation of a real arterial cross-section undergoing rupture in a two-dimensional setting when subjected to inflation pressure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The growth of metastases in the brain increases the state of stress, create leaky blood vessels and disrupt regular brain cells. Essential steps during the development of metastases are the infiltration of the tissue, the nutrient-dependent growth and the stimulation of blood-vessel sprouting. A promising medical treatment can be obtained by the direct infusion of a therapeutic solution into the tissue. Besides experiments, computational models can improve the understanding of brain metastases. In this regard, the liquid-saturated brain tissue represents a porous material. Therefore, the framework of the Theory of Porous Media (TPM) provides an excellent tool for its description. The continuum-mechanical theory of a multi-constituent model and mechanisms of metastases growth are presented in this contribution. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A recent computational model for tumor growth is presented. The mathematical model, based on thermodynamically constrained averaging theory (TCAT), is shortly summarized in the first part; then the attention is focused on modeling hypothesis and their impact on numerical results. Perspectives for future developments of the presented multiphase model are outlined at the end of the paper. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A surgical intervention is often required if the functionality of the sensitive human brain tissue is seriously compromised, e. g., due to the occurrence of malignant brain tumours. A promising method for an effective tumour-treatment procedure is given by the so-called convection-enhanced drug delivery (CED), cf. [1]. In this regard, the aim of this contribution is to simulate the expected effects as well as coupled impacts of a (scheduled) CED-procedure with the help of numerical computations, which base on a sophisticated multiphasic and multi-physical modelling strategy applied to human brain tissue. In particular, a quaternary porous-media model, cf. [3–5], is used for the discussion of selected numerical examples and demonstrates the applicability of the model. In detail, the optimal catheter placement and the application of multiple infusion catheters are studied in terms of the occurring anisotropic therapeutic spreading of the infused drug. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Recently, a scaled boundary finite element (SBFE) formulation for geometrically and physically nonlinear materials has been developed using the scaled boundary finite element method (SBFEM). The SBFE formulation has been employed to describe plane stress problems of notched and unnotched hyperelastic elastomer specimens. In this contribution, the derived SBFE formulation is extended to nonlinear time- and temperature-dependent material behavior. Subsequently, the SBFE formulation is incorporated into a crack propagation scheme to model crack propagation in cyclically loaded elastomer specimens of the so-called tear fatigue analyzer (TFA). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Masonry arch structures, and, more generally, vaulted structures, are traditionally assessed using a well-established approach, such as linear elasticity or limit analysis, whereby system behaviour at the intermediate stage – which occurs when the material's tensile strength has been exceeded but the collapse mechanism has not yet formed – is disregarded. A more accurate interpretation requires a thorough analysis that can take into account the intermediate cracking stage and uses a constitutive law providing a closer approximation to the actual behaviour of the material. In this paper, an evolutionary fracturing process analysis for the stability assessment of masonry arches is presented. This method makes it possible to capture the damaging process that takes place when the conditions evaluated by means of linear elastic analysis no longer apply and before the conditions assessed through limit analysis set in. Furthermore, the way the thrust line is affected by the opening of cracks and the redistribution of internal stresses can be checked numerically. The results obtained with the described approach are compared with a numerical simulation performed with the finite element code Diana (TNO, The Netherlands) adopting discrete cracking with cohesive laws. Finally, the case study of the arch of the Mosca Bridge over the Dora River in Turin, Italy, is described. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: There is currently a gap in the understanding of how crack propagation by intergranular versus transgranular fracture varies with changes in material properties and grain size. Much of the prior work in this area has been in terms of LEFM and criterion based on toughness alone. More recent work has shown that a toughness-and-strength approach is required. In this study a strength-and-energy approach is applied to intergranular-versus-transgranular fracture through a cohesive-zone approach implemented in a finite element model. Results show that intergranular fracture becomes more likely, and has an increasing shear component, as grain toughness increases and grain stiffness and grain size decrease. These results can help guide material development. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Based on the work by Eshelby, the path-independent J k -, M -, L - and interaction- or I k -integrals were introduced and applied to cracks for the accurate calculation of crack tip loading quantities. Applying the FE-method to solve boundary value problems with cracks, numerically inaccurate values are observed within the crack tip region affecting the accuracy of local approaches. Simulating crack paths, local approaches face further problems as cracks are running towards interfaces, internal boundaries or other crack faces. Within global approaches, path-independent integrals are calculated along remote contours far from the crack tip, essentially exploiting numerically reliable data requiring special treatment only for the near-tip crack faces. To provide path-independence, additional integrals along interfaces, internal boundaries and crack faces are necessary. In this paper, new global approaches of path-independent integrals are presented and applied to the calculation of crack paths at two-cracks systems. A second focus is directed to the accurate loading analysis and crack path prediction considering anisotropic properties and material interfaces. The numerical model provides crack paths which are in good agreement with those obtained from crack growth experiments. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Many tools in production technology are nowadays coated to obtain a satisfactory lifetime and degradation resistance. Therefore, the main goal of this study is to investigate antiadhesive and wear resistant coatings made of ceramics, plastics and metals produced by High Power Pulsed Magnetron Sputtering (HPPMS) technique [1]. A cohesive zone element technique (CZ) is applied to model the interactions of the coatings and the substrate surfaces (see [2]). This goes along with the investigations of the delamination and failure behavior of the involved surfaces. To illustrate the applicability of the model, several structural simulations are performed. The developed CZ element model is capable of modeling the separation, the contact and also the irreversible reloading conditions in both normal and tangential directions [3]. The model is further developed to be applicable for different structures including different bonding behaviors, with a higher stability. The talk concludes with a detailed discussion of the numerical results of different material and interface properties. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Hydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot-type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille-type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp-crack discontinuity, the proposed regularized approach has the main advantage of a straight-forward modeling of complex crack patterns including branching. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Common material models that take into account softening effects due to damage encounter the problem of ill-posed boundary value problems if no regularization is applied. This condition leads to a non-unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non-local behavior of the damage [1]. For this purpose a field function is used to couple the local damage parameter to a non-local level, in which differences between the local and non-local parameter as well as the gradient of the non-local parameter can be penalized. In contrast, we present a novel approach to regularization in which no field function is needed [2]. Hereto, the regularization is carried out by means of the divergence of the displacements and no additional quantity is necessary since the displacements are already defined on a non-local level. The idea is that with an increasing value of the damage the element's volume will increase as well. This is a result of the softening due to the occurring damage. The increasing volume can be measured by the divergence of the displacements which can be penalized by an additional energy part. The lack of any field function and the regularization by the use of the divergence of the displacements entails several numerical advantages: the computational effort is considerably reduced and the convergence behavior is improved as well. Naturally, the numerical results are mesh independent due to the regularization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The effects of a circular defect size and position on the post-damage response of the FMLs laminates under compressive loading has been studied. Compression tests are performed on composite plates comprising a hole having different diameters (8 mm, 12 mm and 16 mm) and located at different positions (25%, 50% and 75%) in the loading direction. A numerical analysis using the finite element method FEM has permits the identification of the initiation zones and the description of the damage evolution in these laminates. The results of the numerical simulation are in good agreement with the experimental results. The FEM has well predicted the critical damage zones. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the recent years phase-field modeling of fracture has become a promising tool to describe complex crack patterns in all kinds of solid materials. Many of the models assume an isotropic material behavior, which of course is not a meaningful assumption for e.g. biological tissues such as arterial walls. Since the phase-field approach introduces an additional (smeared) phase describing the evolution of the crack, this method is well suited to be extended to anisotropic materials without thinking about an adaption of the discretization technique. Anisotropy can be incorporated in several ways, like by an extension of the surface energy, i.e. by making the energy release rate orientation dependent, as considered in [1]. Our ansatz is based on a pure geometrical approach, namely on an anisotropic formulation of the crack surface itself. Here, we will focus on transversely isotropic and cubically anisotropic solids, where the latter one makes the incorporation of the second gradient of the crack phase field necessary. At the end one numerical example is shown, which conceptually shows the influence of the anisotropy on the crack path. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this work, crack initiation in elliptically notched plates under uniaxial tension is studied by means of a Finite Fracture Mechanics analysis. The stress concentration factor changes with the aspect ratio of the half axes: from unity for slender ellipses in loading direction to infinity for crack-like ellipses normal to the loading. The closed-form solutions of the stress field and an approximate formulae of the stress intensity factor of mode I cracks allows for an efficient Finite Fracture Mechanics analysis of plates with elliptical notches with arbitrary aspect ratios. The results show that the transition from vanishing stress concentration to infinite (crack-like) stress concentration is rendered continuously by the present approach. A transition from strength of materials to Linear Elastic Fracture Mechanics is obtained that shows distinct size effects. A comparison to experimental results on size effects of notched plates shows good agreement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Subject of the investigation is a two-layered tube under generalized plane strain subject to a combination of internal pressure and an elevated temperature at the inner surface. Criterion for the permissible stress is the yield criterion by von Mises, and the elastic limits are given as well as a way for a straightforward optimization procedure in respect of the weight of the device is shown. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Since the first discovery of quasicrystals in a man made Al-Mn alloy about thirty years ago, people made great effort to investigate this kind of outstanding material. The materials scientists are constantly trying to produce stable quasicrystalline particles or even a complete single quasicrystalline specimen. On the other hand, the fracture behaviour of quasicrystals is started to be investigated because the coupling effect between phonon and phason fields can rebuild the conventional fracture criteria. This work develops a numerical tool for simulating in-plane problems of 1D QC and extends the fracture quantities i.e. stress intensity factors (SIF) and strain energy release rate to phason fields. Finally, numerical results are given to reveal what difference the phason field can bring into conventional fracture quantities. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, a finite element formulation is defined in the framework of the discontinuous Galerkin method. Discontinuous Galerkin (dG) methods are classically used in fluid mechanics, however recently their application in solid mechanics has become more vivid among scientists. Of special interest is their application in elliptic problems with constraints such as incompressibility which leads to volumetric locking phenomenon and also in some structural models of shells, plates and beams with compatibility constraints, which brings about shear locking [1]. While classical standard Galerkin methods must be continuous, dG methods can be applied for discontinuities across element boundaries, where a jump of a value (displacement) can be observed. In the present work, a dG method is applied to a linear elastic bar, where a weak discontinuity is allowed in the bar. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In typical applications as ultrasonic welding horns, the oscillators are designed to be driven in the longitudinal mode. Modal interactions occur at critical aspect ratios, resulting in a poor uniformity of the output surface and assessing the geometry as critical. In this contribution, a method is presented for a simple rectangular disc how to eliminate the modal interaction and decouple the longitudinal mode from other modes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution shows the effectiveness and versatility of the corotational formulation in the development of shell finite elements for geometric and material nonlinear analysis of thin structures. In particular, flat triangular elements especially suited to shell structures made of shape memory alloys (SMA) or soft biological tissues are dealt with. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A T-spline-based isogeometric analysis is applied to frictional contact problems between deformable bodies in the context of large deformations. The continuum is discretized with cubic T-splines and cubic NURBS (Non-Uniform Rational B-Splines) for comparison purposes. A Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the normal and friction contact constraints in the discretized setting. It is demonstrated that the proposed formulation combined with analysis-suitable T-spline interpolations, is a computationally accurate and efficient technology for local and global solutions of contact problems. T-spline analysis models are generated using commercially available T-spline modeling software without intermediate mesh generation or geometry clean-up steps. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The present contribution deals with the mechanics of metallic microlattices from selective laser melting (SLM). Finite element analyses with elasto-plastic material parameters identified in experiments investigate the structural load bearing behavior of different unit cell topologies. Typical failure modes like local buckling as well as global localization in shear bands are analyzed in simulations and experiments for compression tests. Ashby diagrams for the scaling behavior of stiffness and strength at various densities are determined for both bending- and stretch-dominated lattice types. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Cables are complex components consisting of a multi-layer structure and various materials. The structural setup includes for example conducting wires, isolating shields and protecting sheaths. This leads to several inelastic effects under large deformations like pull-out of wires, delamination of layers or friction between the constituents. The materials used in cables belong to different material classes and consequently show different behavior under load. Elastoplastic behavior has to be expected for metallic wires, whereas polymer layers behave viscoelastically. The combination of these inelastic effects caused by the structure and constituents of cables motivates the inclusion of inelasticity in the material model on a phenomenological level. Since cables are flexible, slender structures, they can be described physically correctly by the theory of Cosserat rods. In this context, the constitutive equations are formulated in terms of the sectional quantities. The related model parameters have to be determined in suitable experiments. As cables undergo large multiaxial deformations in applications, uniaxial experiments are not sufficient for their characterization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Residual stresses are important by the manufacturing of the most components. The analysis of residual stresses using the hole-drilling method is complicated and is based at the moment solely on strain measurement on the surface. Now, an approach is described where the residual stresses can be calculated on the basis of strain measured in several plains. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, a well-known law for material damping description (see [1]) is verified. Thereby, material damping is characterized as a function of local stress amplitudes. To identify the resulting structural damping, a calculation of local stresses is necessary. In a first step, an analytical approach is used to calculate the damping on the basis of the stress distribution. In a second step, the local stress distribution of the described structure is calculated using a finite element approach. In this context, damping is calculated using the identified discrete stress values through the structure. By varying the mesh density, the resulting damping is compared to the calculated damping using the analytical results. Finally, it can be seen that the quality of the calculated damping value depends on the quality of the calculated stress value and therefore on the mesh density. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Follower forces on a surface are defined as the forces which are keeping their constant directions with regard to the surface. A typical example is pressure, which is acting always in the direction of the normal. The linearization is necessary in order to solve a problem using an implicit scheme in the case of large deformations. Consider, for example, pressure p acting on a surface s , defined by the vector r (ξ 1 , ξ 2 ). In this case, a weak form is written as: (1) Formally, as shown in [1], [2] the following linearization can be formulated as (2) which is recovering an apparent unsymmetrical structure with regard to Δ u and δ u and, therefore, corresponding unsymmetrical tangent matrix. Though, the system is initially conservative an initially looking unsymmetrical structure is derived due to the linearization of the normal in the Cartesian coordinate system. A special complicated transformation for integrals with closed boundaries was necessary to show the symmetry in this case, see in [3], [4]. Nevertheless, as mentioned by Simo in [5], linearization in a covariant form is always leading to the symmetric structure for conservative systems. Application of the covariant derivation has become a standard tool within the geometrically exact theory of contact interaction, see in [6], [7]. The corresponding symmetry of tangent matrices for all conservative cases is then automatically fulfilled, moreover, they are obtained for all contact pairs such as surface-to-surface, curve-to-curve, curve-to-surface in a close covariant form. Using these transformations, one can treat contact tractions not as unknown variables to be computed, but as given external forces which are keeping their direction in the local coordinate system. This case we can call an inverse contact algorithm . The main results of the geometrically exact theory for contact interactions for surface-to-surface contact pairs are outlined first in order to obtain all relationships for the inverse contact algorithm . (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The contribution is concerned with a numerical method to analyze the mechanical behavior of 3D solids. The method employs directly the geometry defined by the boundary representation modeling technique, which is frequently used in CAD to define solids. It combines the benefits of the isogeometric analysis methodology with the scaled boundary finite element method. In the present approach, only the boundary surfaces of the solid are discretized. No tensor-product structure of three-dimensional objects is exploited to parametrize the physical domain. The weak form is applied only on the boundary surfaces. The governing partial differential equations of elasticity are transformed to an ordinary differential equation (ODE) of Euler type. The isogeometric Galerkin approach is employed to approximate the displacement response at the boundary surfaces. It exploits the two-dimensional NURBS objects to parametrize the boundary surfaces. To solve the Euler type ODE, the NURBS based collocation approach is applied. The accuracy of the method is validated against the analytical solutions. The presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Thanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth – and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a high-order implicit representation of the material interface. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present paper we consider structure-preserving integration methods in the context of mixed finite elements. The used low-order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy-momentum (EM) consistent time-stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu-Washizu-type variational formulation we develop a second-order accurate structure-preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: When using a special forming technology called “Die-Less Hydroforming” to create objects, due to the lack of a conventional forming tool (like a die or a punch) and depending on a particular cutting of the blank geometry, it is possible to generate some special clamping effects when inflating the seal-welded blanks. In our contribution, we present results of a study of these clamping effects in extracts, which have been investigated by means of practical inflating tests as well as numerical forming simulations using LS-DYNA with “Die-Less-Hydroforming”-samples having a special geometry that looks like a “Pac-Man”. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this work, an approach is presented to improve global accuracy properties for physically non-linear problems in the frame of elastoplasticity. The work is motivated by the fact that convergence characteristics of a finite element solution are dominated by the regularity of the exact solution. For a material undergoing inelastic deformations, however, very few analytical solutions for the field variables are known, especially for the displacement field. Considering a simple, one-dimensional example, it is shown that the convergence rates are far from optimal. The reason is explained by establishing ties to a familiar, but more demonstrative problem. In the next section two remedies for the problem, based on the Extended Finite Element Method (XFEM) are presented and discussed, in the last section a 2D-problem is considered. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the framework of solving elastodynamic problems using a least-squares mixed finite element method (LSFEM) the implementation of a stress-velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first-order div – grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L 2 -norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two-dimensional problem. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the context of the particle finite element method (PFEM) a body is considered as a set of particles that are meshed with standard finite elements before every load step. This enables the method to cope with large topological changes where the standard FEM often fails. To mesh the set of particles, its boundary needs to be detected which is accomplished with the α-shape method, and although this method is often used within the PFEM, the crucial parameter α is not well understood. This article provides a physical interpretation of α and shows its meaning in the context of strength of materials. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the present work, we present an experimental characterization of a thermoplastic copolymer made out of Polypropylene and Polyethylene (PP-PE); a polymer that is, for example, used as a core material for layered sandwich composites. The rate-dependence and the temperature-dependence were investigated by means of tensile tests within the large deformation range and by shear tests. The experiments were monitored using a Digital Image Correlation (DIC) system. The main goal of the experimental campaign is related to the development of a constitutive model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Carbon fiber reinforced plastics (CFRP) are mostly used in multilayered laminates, which consist of several very thin layers stacked over each other. For such laminated structures, delamination represents one of the most critical states of failure. In order to predict both the onset as well as the propagation of delamination, a cohesive zone-like continuum damage model is proposed in this paper. This damage model is directly incorporated into a solid-shell finite element with finite thickness. Further, the formulation is capable of considering the interaction of different failure modes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The main goal of the present work is the comparison of the performance of a least-squares mixed finite element formulation where the solution variables (displacements and stresses) are interpolated using different approximation spaces. Basis for the formulation is a weak form resulting from the minimization of a least-squares functional, compare e.g. [1]. As suitable functions for standard interpolation polynomials of Lagrangian type are chosen. For the conforming discretization of the Sobolev space vector-valued Raviart-Thomas interpolation functions, see also [2], are used. The resulting elements are named as P m P k and RT m P k . Here m (stresses) and k (displacements) denote the approximation order of the particular interpolation function. For the comparison we consider a two-dimensional cantilever beam under plain strain conditions and small strain assumptions. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Applications of elastic plates weakened with full-strength holes are of great interest in several mechanical constructions (building practice, in mechanical engineering, shipbuilding, aircraft construction, etc). It's proven that in case of infinite domains the minimum of tangential normal stresses (tangential normal moments) maximal values will be obtained on such contours, where these values maintain constant(the full strength holes). The solvability of these problems allow to control stress optimal distribution at the hole boundary via appropriate hole shape selection. The paper addresses a problem of plane elasticity theory for a doubly connected domain S on the plane z = x + iy , which external boundary is an isosceles trapezoid boundary; the internal boundary is required full-strength hole including the origin of coordinates. In the provided work the unknown full-strength contour and stressed state of the body were determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An analytical model for kink band deformations occurring in laminated composites is proposed based on geometric and potential energy principles. Whilst nonlinear material behaviour and imperfections are included the model considers a symmetric, multi-directional laminate lay-up where the kink band is assumed to occur in the central 0° laminae. First results compared to data in the literature are presented offering encouragement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution discusses the influence of fluid forces, stemming from compliant, contact-free annular rotor seals, on the steady state stability and bifurcation behaviour of a rotor. The model used in this work consists of a Laval-Rotor where the disc runs in a turbulently streamed seal. The compliance of the seal is reduced to a visco-elastically supported outer seal ring. In order to account for the fluid seal forces the Childs-Hirs-model is used. An investigation of the eigenvalues shows that the compliance of the seal support may lead to a significant increase in the stable operating range. A stability-loss via Hopf- , Hopf-Hop f or secondary Hopf- Bifurcations can occur depending on the system parameters. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An established postprocessing procedure for the determination of interlaminar shear and normal stresses based on the results of a conventional shell finite element analysis is generalized for arbitrarily curved laminated shells. The method relies on the three-dimensional equilibrium conditions and an extended lamination theory. Underlying approximations are discussed and exemplary results are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: High-frequency vibrations may be utilized in order to smooth the characteristics of dry friction at low sliding velocities and, consequently, quench undesired friction induced phenomena. Many studies have been published so far, most of them using classical Coulomb friction models and yielding compact results. Unfortunately, the agreement with related experimental results is insufficient. As the Coulomb model overestimates the smoothing effect, improved modelling seems to be necessary. Based on Dahl's friction model, the effect of longitudinal and transverse high-frequency vibrations on a 1-DoF-friction oscillator is investigated here. Accounting for contact compliance, a reduction of the smoothing effect is observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Ultrasonic vibrations in the micrometer amplitude range have been proven to be capable to influence frictional contacts with respect to decreasing friction coefficients in experiments on small test set-ups solely loaded by their small weight [1]. In this paper experimental results on applying this effect to large objects are presented. To get large vibration amplitudes and velocities detailed pre-investigation on the excitation of the structures in contact have been performed. These structures are investigated in a roller rig designed for these purposes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Abstract: The transformation of ambient vibrational energy into electric energy through the use of piezoelectric energy harvesting devices has been the subject of numerous investigations [1]. A commonly studied energy harvesting device performing especially well under broadband excitation, is the piezomagnetoelastic energy harvester investigated by Erturk et al . [2], which is usually discretised for the fundamental vibration mode resulting in a single-mode model. This contribution presents the study of a multi-mode model of the piezomagnetoelastic energy harvester under random excitation. The probabilty density function (PDF) is computed to be the solution of the corresponding Fokker-Planck equation using a Galerkin type method [3,4]. Based on the PDF, the resulting voltage variance is computed as a measurement for the expected power output as demonstrated in [5]. The results of the multi-mode model are then compared with the results of the single-mode model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Most metals fail in a ductile fashion, i.e, fracture is preceded by significant plastic deformation. The modeling of failure in ductile metals must account for complex phenomena at micro-scale, such as nucleation, growth and coalescence of micro-voids. In this work, we start with von-Mises plasticity model without considering void generation. The modeling of macroscopic cracks can be achieved in a convenient way by the continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities [1]. This avoids the use of complex discretization methods for crack discontinuities and can account for complex crack patterns. The key aspect of this work is the extension of the energetic and the stress-based phase field driving force function in brittle fracture to account for a coupled elasto-plastic response in line with our recent work [3]. We develop a new theoretical and computational framework for the phase field modeling of ductile fracture in elastic-plastic solids. To account for large strains, the constitutive model is constructed in the logarithmic strain space, which simplify the model equations and results in a formulation similar to small strains. We demonstrate the modeling capabilities and algorithmic performance of the proposed formulation by representative simulations of ductile failure mechanisms in metals. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Metal sheet forming processes like deep drawing are applied in order to produce carriage parts in mass production. Therefore, forming tools are required that are well protected against wear. For such forming tools, wear resistant surfaces are, e.g., produced by thermal spraying of hard material coatings. The thermal spraying process itself is a highly transient thermo-mechanical process. In order to gain a better understanding of the heat input and transfer during thermal spraying, a simulation framework for thermal spraying processes is presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Light-weight robots and manipulators stand out due to their very good weight-to-load ratio and a low energy consumption. Unfortunately, the light-weight design yields a lower stiffness, which results in undesired elastic deformations, especially during high-speed working motion. One way to limit these unwanted oscillations can be implemented with modifications of the command signals, e.g. by input shaping or pre-computed feed-forward control. However, a feedback control-concept has the ability to provide a fast compensation of elastic deformations due to high-speed working motions or in case of unwanted environment contact as well as in the presence of other external disturbances. In this contribution, an active damping control (ADC) for fast moving manipulators with significant structural elasticities is presented. This approach does not require additional actuators and it is suitable for a large variety of manipulators that exhibit structural vibrations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this study, modal analysis of vehicle power trains is based on the linearization of the underlying equations of motions at specified time instants. The equations of motion represent a flexible multi-body system where force-elements (joints) connect different bodies. Whenever the linearization leads to an ordinary differential equation with constant coefficients, a standard eigenvalue procedure is used, to compute eigenvalues and mode shapes. The concept is applied to a vehicle power train. Comparison of the results with a commercial software product provide good agreement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The constitutive modelling of skeletal muscle tissue in a continuum-mechanical framework demands the consideration of many complex material characteristics. This complexity stems from the microscopic arrangement of different structural elements, such as, for example, sarcomeres and connective tissue. The former are responsible for the active contractile behaviour while the latter are mainly responsible for the passive stiffness of the muscle tissue. Thus, it is highly challenging to build appropriate macroscopic models based on phenomenological descriptions and yet cover most of the complex material behaviour. Strain-energy functions have to be adapted for every significant material phenomena coming from experimental testing of muscle tissue. Another way to treat the modelling of active muscle tissue is to describe important parts of the heterogeneous microstructure and use homogenisation approaches to derive effective overall properties. This contribution aims to investigate and develop new homogenisation techniques for passive skeletal muscle tissue and is the first step towards the ultimate goal of developing a consistent framework that allows to derive macroscopic material properties for active muscle tissue based on microstructural characteristics. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Recently a new computational model, based on the thermodynamically constrained averaging theory, has been proposed to predict tumor initiation and proliferation and afterwards to study plantar tissue mechanics. The foot tissue is modeled as an elastic porous medium, in large strain regime and completely filled by a fluid phase. By considering the interstitial fluid, it is possible to mimic the viscoelastic behavior of the plantar tissue observed experimentally. Being the global response of the bi-phase system viscoelastic, it is shown that the duration of stance as well as of each of gait cycle has an influence on tissue stress field. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution an approach for the fiber reorientation in three-dimensional arterial walls is presented. In detail the load-bearing capacity of the tissue is increased by re orienting the fibers with respect to the principal stresses, cf. [1]. The improved fiber reorientation algorithm is combined with the polyconvex nonlinear anisotropic material model presented in [3]. The results of a three-dimensional finite element simulation, where the reorientation approach is applied to a short segment of a patient-specific arterial geometry, are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution presents a micro-mechanically motivated, time-dependent constitutive model of soft biological tissues. It considers seperate contributions of the matrix material, collagen fibrils, proteoglycans (PGs) as well as their interactions. It is based on the observations [6], that PG bridges facilitate sliding between fibrils. The initial overlapping lengths of the PG bridges are statistically distributed and decrease due to slippage. A linear-elastic force response of a PG bridge is assumed. Damage of the PG bridges is reversible and decays over time (cf. Gupta et al. [1]). This behaviour is taken into account by a healing model based on the evolution of the overlapping length. The damage of the PG bridges decreases the PG density and in turn increases the fibril contact, leading to fibril stretch. The strain energy function of fibrils is based on the response of single tropocollagen molecules and takes both, an entropic and an energetic regime into account. At higher strains, fibrils can additionally undergo damage, which in contrast to the PG damage is irreversible. The so obtained constitutive model is capable to predict several mechanical phenomena of soft tissues, such as non-linearity, Mullins effect, hysteresis and permanent set. Finally the model is compared against experimental data available in the literature. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Biomechanical simulations of the female breast are important for surgical applications such as implants augmentation, tumorectomy and reconstruction after the tumor removal. One of the main challenges for such breast simulations is to define its reference configuration which can be considered as a stress free state. Indeed, MRI (Magnetic Resonance Imaging) scans of the breast can be obtained only under gravitational load which introduces a considerable stress and strains level for any position of the patient. Moreover, realistic material properties especially anisotropy of skin should be taken into account. This anisotropy can play an important role but has not so far been considered in biomechanical simulations of the breast. In the current contribution, we implement an iterative method to define the reference configuration of the breast model according to MRI data of certain individuals in the prone position by taking into account the anisotropy directions of skin. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A method to incorporate residual stresses in arteries, based on the assumption of smooth transmural stress measure distributions with slight slopes, is discussed. The artery is first loaded with the internal blood pressure without considering any residual stresses. With help of suitable stress invariants and volume averaged mean values on specific sectors domains, the stress gradient is iteratively decreased in radial direction. In order to assess the accuracy of the method, a three-dimensional patient-specific arterial geometry, suffering from atherosclerosis, is considered. These was reconstructed from ultrasound based medical imaging, see [2]. Moreover, the radially sliced arteries can be loaded exclusively with the calculated residual stresses in order to predict the opening angle. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In numerical simulations with the finite element method the dependency on the mesh – and for time-dependent problems on the time discretization – arises. Adaptive refinements in space (and time) based on goal-oriented error estimation [1] become more and more popular for finite element analyses to balance computational effort and accuracy of the solution. The introduction of a goal quantity of interest defines a dual problem which has to be solved to estimate the error with respect to it. Often such procedures are based on a space-time Galerkin framework for instationary problems [2]. Discretization results in systems of equations in which the unknowns are nodal values. Contrary, in current finite element implementations for path-dependent problems some quantities storing information about the path-dependence are located at the integration points of the finite elements [3], e.g. plastic strains etc. In this contribution we propose an approach – similar to [4] for sensitivity analysis – for the approximation of the dual problem which mainly maintains the structure of current finite element implementations for path-dependent problems. Here, the dual problem is introduced after discretization. A numerical example illustrates the approach. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution we investigate a bistable energy harvester with regard to its optimal impedance load. A bistable energy harvester exhibits three different types of oscillation: Single-well (about a stable equilibrium), cross-well (between the wells) and inter-well (about the unstable equilibrium). The occurring oscillation type depends, for instance, on the excitation parameters and the initial conditions. It has already been observed ( [1]) that the optimal impedance, which allows to maximize the power output, varies for each oscillation type. In our investigations we complement these findings with analytical and numerical calculations. For our analysis we examine the non-dimensionalized coupled equations of a bistable energy harvester. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: To accelerate the development of non-linear, friction-excited systems, i.e. automotive friction brakes, novel test procedures are being developed. These include the study of the system's forced vibrations. However, there is a lack of knowledge concerning feasible test procedures, the assessment of the gathered data, and the possible vibration phenomena. In this context, the contribution at hand discusses vibrations in non-linear, forced, friction-excited systems. In the pre-flutter regime proposed criteria for identification of parameter regions in which limit cycle oscillations can occur are challenged. In the post-flutter regime frequency spectra for different excitation conditions are studied. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The directional solidification (DS) of the eutectic alloy NiAl-9Mo (at. %) leads to a formation of single-crystal molybdenum-rich fibers embedded in a NiAl matrix and has promising high-temperature properties. Material models describing each phase are necessary to be able to predict the materials behavior of the in-situ composite under several conditions. Using a one-dimensional Voigt-Taylor model based on a phenomenological approach, the creep behavior is simulated and the results are compared to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We investigate the bifurcating solutions at a Hopf–Hopf interaction point with an internal 1 : 3 resonance. It turns out, that the transitions from single to mixed modes can be described by Duffing or Mathieu szenarios. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Fiber reinforced plastics such as carbon fiber-reinforced composites are typically characterized by their high siffness to weight ratio making them particularly attractive in lightweight construction. In addition, the architecture of these materials means that the correct modelling of their orthotropy is very important. In this work, volume averaged stress-strain responses are generated from a micro representative volume element (RVE). A nonlinear macro constitutive material model accounting for anisotropic plasticity is proposed. The model is fitted and compared to the micro stress-strain response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the framework of linear elasticity, singularities occur in domains with non-smooth boundaries. Particularly in Fracture Mechanics, the local stress field near stress concentrations is of interest. In this work, singularities at re-entrant corners or sharp notches in Reissner-Mindlin plates are studied. Therefore, an asymptotic solution of the governing system of partial differential equations is obtained by using a complex potential approach which allows for an efficient calculation of the singularity exponent λ. The effect of the notch opening angle and the boundary conditions on the singularity exponent is discussed. The results show, that it can be distinguished between singularities for symmetric and antisymmetric loading and between singularities of the bending moments and the transverse shear forces. Also, stronger singularities than the classical crack tip singularity with free crack faces are observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Model reduction in car crash simulations is a fairly new research field. In this paper, a possible workflow is presented: Since nonlinear behavior can occur, parts with linear and nonlinear behavior need to be separated with clustering methods such as k-means or spectral clustering. For the latter, a nonlinear reduction technique such as POD-DEIM needs to be applied. A longitudinal chassis beam of a 2001 Ford Taurus is used to examine the different clustering methods. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This article presents a continuum damage mechanics approach to characterize fatigue mechanisms of cord-rubber composites. An airspring bellow which consists of layers of rubber and reinforcing cords is considered for this work. The phenomenological material model for rubber is formulated for the purpose of analyzing the rate dependent behavior under cyclic loading. The rate dependency and hysteretic behavior are characterized by using the concept of internal variables [1]. The implementation of the constitutive formulation for rubber material is done in ABAQUS via UMAT. A fatigue failure mechanisms of cord-reinforced airspring is for example interfacial debonding. Within the framework of finite element cohesive zone modeling, a user element is developed to study the cord-rubber interfacial debonding. Furthermore, the developed methodology can be easily extended to understand the long-term effects of e.g. temperature, frequency, loading rates, amplitudes etc. on the fatigue life of airsprings. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: For many crack geometries the standard XFEM may lead to badly conditioned equation systems. Recently a number of remedies to that problem have been published. In this contribution the stabilization technique presented in [1] is extended to dynamic and possibly nonlinear fracture mechanics and additionally combined with the SGFEM / SXFEM [2]. The performance of the different strategies is demonstrated in a linear elastic 3D mode 1 crack problem for which the analytical solution exists. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic-brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit-explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit-explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Modeling the damage of brittle materials is of great importance considering a variety of structural components. Prominent examples are high strength engineering ceramics. The present work is concerned with silicon nitride, a material with increasing relevance in industrial applications. In the sense of a hierarchical model structure, effective properties of micromechanical simulations were applied to macroscopic, phenomenological damage models for monotonous and cyclic loading. In the following, both models are introduced and the application of the cyclic damage model to a four point bending test is discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The computation of stress intensity factors (SIFs) by crack opening displacements (CODs) is discussed in linear elastic fracture mechanics (LEFM) with stressfree crack surfaces, in the context of the extended finite element method (XFEM) and a hybrid explicit-implicit crack description. Herein, the approximated CODs are compared with the expected openings for a pure mode I , II and III . The analytical modes are evaluated in a reference coordinate system, which is aligned with the (curved) crack surface and extracted from the implicit level-set functions. This approach allows without any significant modifications, an intuitive and efficient computation of SIFs in 2D and 3D even of curved cracks. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the phase field approach for fracture an additional scalar field is introduced in order to describe the state of the material between intact and fully broken. So far, for the loading dependent degradation of stiffness (damage) either the volumetric-deviatoric split of strain [1, 2] or the spectral decomposition [3, 4] is used. In contrast to such an isotropic degradation of stiffness, the fully broken state represents a crack with a particular orientation. Both aforementioned approaches do not take the crack orientation into account. This may lead to the violation of the crack boundary conditions. In order to satisfy these conditions the phase field approach is modified here by taking the orientation of the crack into account. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution focuses on the sequential laminate-based modelling approach for the numerical simulation of the complex electromechanical material behaviour of ferroelectric single crystals. The construction of engineered domain configurations by using the method of sequential lamination in order to study the domain evolution and polarisation switching in ferroelectric single crystals has recently been carried out in the works of [1–4]. By fulfilling the kinematic and polarisation compatibility conditions between the domain structures in a crystal, the proposed laminate-based formulation is governed by an energy-enthalpy function and by a dissipation potential. The mixed energy-enthalpy, written in terms of the total strains, electric field and a set of internal variables, here the multi-rank laminate volume fractions, governs the dissipative electromechanical response of the ferroelectric crystal, whereas the rate-dependent dissipation potential formulated in terms of the flux of the internal variables describes the time-dependent evolution of the multi-rank laminate volume fractions, subjected to inequality constraints. The model reproduces experimentally observed hysteresis and butterfly curves, characteristic for single crystal ferroelectric materials, when subjected to homogeneous electromechanical loading conditions. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We consider the Γ-limit, as the number of particles diverges, of the energy per particle of a one-dimensional ferromagnetic/anti-ferromag frustrated S 1 (or S 2 ) spin chain close to the helimagnet/ferromagnet transition point discussing the emergence of chirality transitions. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Soft matter electro-elastic, magneto-elastic and magneto-electro-elastic composites exhibit coupled material behavior at large strains. Examples are electro-active polymers and magneto-rheological elastomers, which respond by a deformation to applied electric or magnetic fields, and are used in advanced industrial environments as sensors and actuators. Polymer-based magneto-electro-elastic composites are a new class of tailor-made materials with promising future applications. Here, a magneto-electric coupling effect is achieved as a homogenized macro-response of the composite with electro-active and magneto-active constituents. These soft composite materials show different types of instability phenomena, which even might be exploited for future enhancement of their performance. This covers micro-structural instabilities, such as buckling of micro-fibers or particles, as well as material instabilities in the form of limit-points in the local constitutive response. Here, the homogenization-based scale bridging links long wavelength micro-structural instabilities to material instabilities at the macro-scale. This work outlines a comprehensive framework of an energy-based homogenization in electro-magneto-mechanics, which allows a tracking of postcritical solution paths such as those related to pull-in instabilities. Representative simulations demonstrate a tracking of inhomogenous composites, showing the development of postcritical zones in the microstructure and a possible instable homogenized material response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The simulation of ferroelectric materials on the atomistic length scale is getting more and more important due to recent advancements in related manufacturing technologies. Therefore, we present an extended molecular statics algorithm in order to not only compute equilibrium configurations efficiently but also to consider the deformation of a discrete particle system due to macroscopic stress. Furthermore, we discuss the impact of mechanical stress and strain on the spontaneous polarization and the magnitude of the coercive field of a ferroelectric barium titanate system. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper we present a time stepping scheme which is based on a variational integrator. This higher-order time stepping scheme includes constraints and a viscoelastic material formulation. A variational integrator is structure-preserving which results from using a discrete variational principle. Therefore, a variational integrator always takes the form of discrete EULER-LAGRANGE equations or the equivalent position-momentum equations. In this framework, we consider the motion of a flexible rope with non-holonomic constraints by the LAGRANGE-multiplier technique. The time stepping scheme is derived from a space-time discretization of HAMILTON's principle. The space discretization is based on one-dimensional linear LAGRANGE polynomials, whereas the time discretization is based on higher-order polynomials and higher-order quadrature rules. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems where state trajectories are constrained to evolve within time-varying, closed, and convex sets. The first main result states sufficient conditions for existence and uniqueness of solutions in such systems. We then design a static state feedback control law using the internal model principle, which results in a well-posed closed-loop system and solves the regulation problem. As an application, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution presents the excitation mechanism of an experimental set-up for measuring the structural behavior of an electric guitar body using Laser-Doppler-Vibrometers, to be compared to the generated sound. It is the aim of this investigation to gain insight into the influence on the sound of materials and designs of the large variety of commercially available electric guitars. The core of the experimental set-up is the excitation mechanism, which has been developed to guarantee a well-defined and absolute reproducible excitation of the guitar string in order to detect even small differences in sound. This mechanism has been constructed making use of the methods of multibody dynamics and optimization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: This contribution presents an alternative numerical method on how to find the cavitation region in elastohydrodynamic (EHD) lubrication using an augmented Lagrangian approach. A theoretical framework for the use of a projection formulation instead of a Linear Complementarity Problem (LCP) is given and the application to multibody systems with EHD contacts is shown. With this new formulation the cavitation condition can be covered by an additional algebraic equation. The projection formulation is applied to the steady-state as well as to the dynamic, mass conservative treatment of the cavitation problem. A numerical verification is given for a rigid rotor with unbalance in an elastic bearing. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Model order reduction (MOR) techniques that project onto a general subspace are common practice. In Elastic Multi-Body-Dynamics (EMBD) distinct interface coordinates are required for the interconnection of the elastic structure and the multi-body system. For that reason, a physical interpretation of the coordinates is mandatory, which is not the case for reduced order models in a general subspace. To make alternative MOR techniques accessible for EMBD, a back-projection approach was introduced by [1]. Therein, the system is projected back onto the physical configuration space, which requires the inversion of the master partition of the projection matrix. But the procedure lacks of robustness and generality. A novel approach is introduced by generating additional master coordinates using sensor placement methods, e.g. the Effective-Independence-algorithm (EfI) [2]. By using a rank criterion for the automatic selection of additional coordinates, the improved back-transformation performs properly and without damaging the reduced order model at a fairly small computational overhead, which is demonstrated at the example of a gear box housing. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The information on the routing of a road provided by a navigation system can be used by the driver of a vehicle with adaptive shock absorber to decide either for optimal comfort or optimal safety depending on the course of the guideway. However, the assessment criteria comfort and safety are with respect to the shock absorber in conflict with each other. In particular, maximal safety on a curvaceous road results in lower comfort. Thus, deciding on high safety means low comfort conveying a warning to the driver to reduce the speed. The methods applied in this paper originate from multibody dynamics, and they are extended by the stochastic road unevenness and the guideway curvature available to the driver from a navigation system using GPS data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The 3-ball Newton's cradle is used as a stepping stone to divulge the structure of impact laws. A continuous cone-wise linear impact law which maps the pre-impact contact velocities to the post-impact contact velocities is proposed for the 3-ball Newton's cradle. The proposed impact law is kinematically, kinetically, and energetically consistent. It reproduces all the classical experimental outcomes. Moreover, the impact law has the mathematical property of being non-expansive. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Kinematically redundant serial robots have become industrially important due their increased workspace and their inherent capability of null space motion resulting in remarkable adaptiveness to specific tasks compared to conventional, non-redundant manipulators. Attempting to increase the cost-effectiveness of industrial processes, introducing minimum-time trajectories may yield economical advantages due to reduced motion cycle times. This contribution presents a method that uses joint space decomposition and analytic inverse kinematics as well as standard optimization techniques to obtain minimum-time B-spline joint trajectories along prescribed task space paths for kinematically redundant serial robots. It is shown that the present method was successfully applied to a planar manipulator. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A trajectory-tracking approach for a parallel kinematic manipulator with flexible links is investigated with respect to its robustness to undesired initial oscillations. For this purpose, an inverse fuzzy arithmetical scheme is presented and applied, in order to estimate allowable bounds on the initial conditions such that a certain tolerance band around the desired trajectory is not violated. The uncertainty bounds on the initial conditions obtained from this identification procedure indicate the influence of the disturbances on the tracking error, and thus also the robustness and the performance of the control scheme. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An impulse-based control scheme for a simple spring-mass oscillator subject to set-valued friction forces is presented. In contrast to PD or PID control laws, the proposed control law prevents non-zero steady state errors and limit cycles. Motivated by Wouw and Leine [1], it is shown that impulse-based control laws can lead to satisfactory behavior if the oscillator starts sticking. In order to realize a practical implementation, the equations of motion are extended by a mathematical model of the actuator dynamics. The analysis is undertaken in the framework of nonsmooth mechanical systems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this contribution, several extensions of the relaxed incremental variational damage model by BALZANI & ORTIZ [1] are provided, in order to appropriately account for the description of arterial tissues. In particular, the one-dimensional formulation from [1] is combined with a numerical homogenization scheme. Moreover, hysteresis behavior is included and a new optimization strategy is used to determine the bifurcation parameters when checking for a loss of convexity. The performance of the proposed model is demonstrated in a three-dimensional finite element simulation of a overstretched simplified atherosclerotic artery. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: The self-reproduction ability of mitotic cells results in an increase of the number of cells with the same characteristics in living bodies. While cells grow in volume and divide themselves, the living body consequently grows in mass and volume. Further, if the factors which regulate the growth process are inhomogeneously distributed, growth takes place at different rates and directions. In this work we aim to provide a new continuum model for growing tissues. More specifically, the model considers the reorientation of the cell-division plane in mitotic cells depending on the stress field of the growing body. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Kinematic analysis, in contrast to sophisticated molecular dynamics simulations, can provide high-level insights into conformational diversity of proteins and other biomolecules, with broad implications for human health. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity. While existing combinatorial constraint counting is limited to generic structures, our geometric approach is also valid for non-generic linkages. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We tackle the fluid transport problem in vascularized tumors by solving a double Darcy model obtained via multiscale homogenization. The hydraulic conductivities of the capillary and interstitial compartments are computed solving classical problems on the representative periodic cell, which encodes details of the microvasculature. Microvascular tortuosity leads to a dramatic decrease of the capillary hydraulic conductivity, and the corresponding lowering in the pressure drop impairs tumor blood flow and consequently advection of molecules. Further perspectives for anti-cancer agents delivery are illustrated. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In the frame of stress based topology optimisation multi-material structures are investigated. At the interface of dissimilar materials an adhesive joint shall be considered. Selecting a continuum approach to model the two adherends and the adhesive, stress singularities occur at the material-interfaces due to the difference in the impedance [1]. This contribution investigates a geometrical opportunity to remove singularities at the interface of two different linear elastic structures. Sensitivities of important parameters are qualitatively shown by a simple example consisting of two cubes under tension. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: An electro-mechanically coupled phase field model for domain evolution in ferroelectric materials is presented. The inner length scale introduced by the model gives rise to size effects, especially in the context of the poling behavior of polycrystals. Such size effects are investigated by 2D numerical simulations for barium titanate polycrystals. Ferroelectric hysteresis curves and coercive fields are calculated for two different transition conditions for the order parameter at the grain boundaries. The results show that there is a significant size effect for the investigated polycrystal systems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: Volume 15 (2015) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 86th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, held 23 – 27 March 2015 at the University of Salento in Lecce, Italy. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections Minisymposia M 1 Multi-Scale Modeling of Ferroic Functional Materials M 2 Applications of the Virtual Element Method M 3 Topological Defects in Solids M 4 Optimal Control and Hybrid Systems M 5 Mechanics in an Interdisciplinary, Multiphysics Environment, Transforming Materials Sciences and Biology 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 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 for differential equations 19 Optimization of differential equations 20 Dynamics and control 21 Mathematical image processing 22 Scientific computing 23 Applied operator theory 24 History of mechanics Young Researchers' Minisymposia YR 1 Analysis, Applications and Approximation of Constrained PDEs YR 2 Phase Field Modeling in Mechanics and Applied Mathematics YR 3 Discretization Aspects in PDE Constrained Optimization YR 4 Co-/Sparsity, Inverse Problems and Compressive Imaging YR 5 Topics in Low-rank Tensor Approximation

Description: Mixed integer control systems are used to model dynamical behavior that can change instantly, for example a driving car with different gears. Changing a gear corresponds to an instant change of the differential equation what is achieved in the model by changing the value of the integer control function. The optimal control of a mixed integer control system by a discretize-then-optimize approach leads to a mixed integer optimization problem that is not differentiable with respect to the integer variables, such that gradient based optimization methods can not be applied. In this work, differentiability with respect to all optimization variables is achieved by reformulating the mixed integer optimal control problem (MIOCP). A fixed integer control function and a time transformation are introduced. The combination of both allows to change the sequence of active differential equations by partially deactivating the fixed integer control function. In contrast to other works, here different fixed integer control functions are taken into account. Advantages of so called control consistent (CC) fixed integer control functions are discussed and confirmed on a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: We consider the problem of underground flow simulations in fractured media. This is a large scale, heterogeneous multi-scale phenomenon involving very complex geological configurations. Within the Discrete Fracture Network (DFN) model, we focus on the resolution of the steady-state flow in large fracture networks. Exploiting the peculiarity of the Virtual Element Method (VEM), which allows the use of rather general polygonal mesh elements, we propose an approach for building a suitable mesh for representing the solution on DFNs. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: In this paper, the mechanics of soft tissues is modeled by introducing a novel polyconvex strain-energy function able to include tissue structured hierarchical arrangement and by reducing model complexity via multiscale homogenization techniques. The case of arterial tissue is successfully addressed by obtaining a quantitative prediction of the age-dependent alterations in aorta mechanics incorporating histological remodeling mechanisms and biochemical variations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Description: A multiscale micromechanical model for soft tissue is presented. This model accounts for the progressive stiffening of the mechanical response due to load-induced microstructural rearrangements of the fibers within the microstructure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)