bluuebunny/crossref_metadata_2025 huggingface dataset:
Topology Optimization with Isogeometric Analysis and Phase Field Modeling
Authors: Muench Ingo , Klassen Markus , Wagner Werner
Published: November 2019

We use a Phase Field Model (PFM) for the evolution of load‐bearing structures on base of the equivalent stress criterion. Similar to Evolutionary Structural Optimization, the equivalent stress from all integration points is collected to evaluate a threshold. The approach couples density and stiffness to the phase field variable. The topology evolves from homogeneously filled regions by nucleation of holes. In numerical examples we compare results using standard Finite Elements (FEM) and Isogeometric Analysis (IGA), respectively. Latter allows for higher continuity between elements, which is essential to avoid the well‐known mesh‐pinning effect.
On the relaxation of continuity conditions for finite element schemes based on a least‐squares approach
Authors: Igelbüscher Maximilian , Schröder Jörg
Published: November 2019

The proposed contribution is based on the idea of the relaxation of continuity conditions and an enforcement of these continuity constraints for the considered fields via Lagrange multipliers. Therefore, a stress‐displacement least‐squares formulation

is considered, which is defined by the squared

‐norm applied to the first‐order system of differential equations, given by the balance of momentum and the constitutive equation, compare for the case of linear elasticity e.g. [1], as well as an additional (mathematically redundant) residual for enforcement of the stress symmetry condition. In general the assumptions for the continuity conditions are related to the conforming discretization of the individual fields. The conforming discretization, which demands continuity of the displacements and normal continuity of the stresses, is given by polynomial functions of Lagrange type for the displacements, i.e.

, and a stress approximation with Raviart‐Thomas functions, i.e.

. A non‐conforming discretization of the stresses considering discontinuous Raviart‐Thomas approximation functions with

yield to a relaxation of the continuity conditions. However the fulfillment of these relaxed constraints is enforced by the introduction of Lagrange multiplier within the underlying least‐squares formulation.
Numerical study of nonlinear elastic wave propagation in locally damaged engineering structures
Authors: Ankay Benjamin , Zhang Chuanzeng
Published: November 2019

In this paper, the two‐dimensional (2‐D) ultrasonic wave propagation problem in an elastic half‐space with a localized damaged zone is numerically simulated by a mapped Chebyshev pseudo‐spectral collocation method [1]. The considered damaged zone, which is embedded in an undamaged host medium, is modelled by a nonlinear elastic and viscoelastic constitutive law. Classical nonlinear elastic and nonclassical hysteretic material behaviors are separately considered and evaluated. In particular, the classical nonlinear elasticity theory of Murnaghan [2] is implemented, while the hysteretic material behavior is modelled by the Duhem‐model. To transfer the constitutive relations from the one‐dimensional (1‐D) to the 2‐D case the Kelvin decomposition method is used. Furthermore, Convolutional Perfectly Matched Layers (CPML's) are used to simulate the semi‐infinite elastic half‐space. The computed time‐domain signals are transformed to the frequency‐domain and subsequently analyzed for different degrees of the wave attenuation and nonlinearity in the damage zone. The applications of the nonlinear ultrasonic technique are discussed based on the numerical results.
A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow
Authors: Matthes Daniel , Cances Clement , Nabet Flore
Published: November 2019

Existence of solutions to a non‐local Cahn‐Hilliard model with degenerate mobility is considered. The PDE is written as a gradient flow with respect to the L2‐Wasserstein metric for two components that are coupled by an incompressibility constraint. Approximating solutions are constructed by means of an implicit discretization in time and variational methods.
Towards deep learned constitutive models based on two‐dimensional strain fields
Authors: Hillgärtner Markus , Linka Kevin , Abdolazizi Kian P. , Itskov Mikhail
Published: November 2019

In order to calibrate material models, experimental stress‐strain curves are usually compared with model predictions under the same loading conditions. While this approach guarantees good results for one specific loading type, the resulting model is not generally able to properly predict other loading scenarios. Therefore, a variety of mechanical tests can be conducted, amongst which uniaxial tension, uniaxial compression, pure‐shear and equibiaxial tension tests are the most commonly used ones. Multi‐axial loading often cannot be adequately predicted solely based on test data from one such experiment. Therefore, the material model can be fitted against several mechanical test data sets simultaneously in order to increase the prediction quality, which requires a considerable amount of experiment work.

This contribution aims to create phenomenological material models which are directly fitted against an experimental force response and the corresponding two‐dimensional strain field obtained from arbitrary loading. To this end, a deep learning framework based on a multilayer‐perceptron (MLP) approach [2] is proposed which identifies suitable strain‐energy functions and their corresponding derivatives. These can be utilized in a commercial finite element code via a user defined material subroutine in order to compare the quality of the approximation with the reference data. This approach avoids the above mentioned idealized experiments and simplifies the process of phenomenological modeling by exploiting the capabilities of deep neural networks.
Stabilization of underactuated nonlinear systems to non‐feasible curves
Authors: Grushkovskaya Victoria , Zuyev Alexander
Published: November 2019

This paper focuses on the development of stability conditions for systems of nonlinear non‐autonomous ordinary differential equations and their applications to control problems. We present a novel approach for the study of asymptotic stability properties for nonlinear non‐autonomous systems based on considering a parameterized family of sets. The proposed approach allows to state asymptotic stability conditions for a family of sets representing the level sets of a time‐varying Lyapunov function and to estimate the rate of convergence of solutions to a prescribed neighbourhood of the given curve. The obtained stability results are applied to the trajectory tracking problem for a class of nonholonomic systems.
Computational modeling of adhesive contact between a virus and a cell during receptor driven endocytosis
Authors: Wiegold Tillmann , Klinge Sandra , Gilbert Robert P. , Holzapfel Gerhard A.
Published: November 2019

The present contribution deals with the viral entry into a cell dictated by the change of the receptor density. While the receptors of the virus are considered to be fixed on its surface, the ones of the cell are mobile within its membrane. Upon contact, a locally increased receptor density of the cell is required, which causes it to diffuse towards the virus. The membrane inflicts and forms an envelope around the virus in the contact zone. The described problem is simulated on the basis of the assumption that the differential equation typical of the heat transport is suitable to describe the diffusion of receptors. Furthermore, two boundary conditions are proposed. The first condition deals with the balance of fluxes on the front of the adhesion zone, where the velocity is supposed to be proportional to the gradient of the chemical potential. The second condition represents the energy balance equation with contributions due to the binding of receptors, the free energy of the membrane, its curvature and the kinetic energy due to the motion of the front. The selected numerical example shows the change of the receptor density over the membrane as well as the motion of the front of the adhesion zone. Special attention is paid to the mobility of the receptors.
A finite fracture mechanics approach for interlaminar crack initiation using the scaled boundary finite element method
Authors: Dölling Sebastian , Bremm Sophia , Hell Sascha , Becker Wilfried
Published: November 2019

In the present study, crack initiation induced by the free‐edge effect in symmetric angle‐ply laminates is investigated. For this purpose, the coupled stress and energy criterion within the framework of finite fracture mechanics is used. In order to obtain the required quantities efficiently the semi‐analytical scaled boundary finite element method is implemented. The obtained effective failure stresses are compared to experimental findings from literature.
Phase field modeling with IGA and FEM: Error surveillance in the transition zone
Authors: Klassen Markus , Muench Ingo , Klinkel Sven
Published: November 2019

The present contribution compares the solution of a phase field problem by the finite element method (FEM) with isogeometric analysis (IGA). For the sake of simplicity, the coupling to additional fields is neglected. Thus, the phase field variable appears as the only unknown in the boundary value problem. The numerical solutions are compared to the analytical solution, elaborated by Falk, of the Allen‐Cahn equation. In this model, the Ginzburg‐Landau free energy density combines a free Landau energy of sixth order with a quadratic gradient energy. The benchmark consists of a simple quadrilateral geometry with boundary conditions for the phase field variable which allows to solve static unidirectional phase transitions. For the FEM, the mesh is refined uniformly in space by h‐ and p‐refinement. In IGA, the refinement is realized by the knot insertion and order elevation algorithms from computer aided design (CAD) which is known as k‐refinement. Furthermore, IGA allows for a higher continuity between the elements which enhances the gradient of the phase transition variable.
Role of diameter and percentage of SMA bars as reinforcement in strength and residual displacement of concrete beams
Authors: Molod Mohammad Amin , Barthold Franz-Joseph , Spyridis Panagiotis
Published: November 2019

Shape memory alloy (SMA) is a smart material that is currently used in reinforced concrete members. This preliminary research aims to numerically investigate the role of diameter and percentage of SMA as the main reinforcement of concrete beam in increasing stiffness and reduction of residual displacement. To do so, eight beams with same geometry and boundary condition reinforced with superelastic SMA under two cycle of four‐point bending loading in Ansys APDL have been simulated. Results showed that enhancement of ratio of SMA in the beams will reduce residual displacement and increase stiffness of the beams. Furthermore, for beams with same percentage of SMA bars, more number of bars with thinner diameters leaded to less residual displacement compared to less number of bars with thicker diameters.
Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells
Authors: Ju Xiaozhe , Mahnken Rolf
Published: November 2019

The increasing use of heterogeneous materials like composites in the industrial praxis has made the finite element (FE) simulation using homogenization techniques a well‐accepted and often even inevitable tool. For a reliable simulation, both discretization and model error need to be controlled. Aiming at a user‐defined target functional called quantity of interest, error estimators are derived using duality arguments. Model adaptivity is established on the macro scale, towards an economic model distribution that exploits the advantages of mean‐field and computational homogenization methods based on unit cells of increasing size. This is achieved by using the same philosophy of adaptive finite element method (FEM) for an economic mesh, which applies simultaneously to model adaptivity. A numerical example shows the effectiveness of the adaptive approach.
Parameter Study of Turbulent Drag Reduction by Spanwise Traveling Transversal Surface Waves
Authors: Albers Marian , Meysonnat Pascal S. , Fernex Daniel , Semaan Richard , Noack Bernd R. , Schröder Wolfgang
Published: November 2019

Large‐eddy simulations of spanwise traveling transversal surface waves in turbulent boundary layer flow are conducted. The parameter space of period, amplitude, and wavelength is investigated by 80 simulations. A maximum decrease of the averaged drag by 26 percent is obtained and an approximate scaling law for the decrease of the skin friction is found.
Optimisation of Diffusion Driven Degradation Processes
Authors: Waschinsky Navina , Barthold Franz-Joseph , Menzel Andreas
Published: November 2019

Nature strives for optimal processes in order to prevent early damage or failure, for example bones which regulate the tissue in high stress areas or the optimal shape of trees. Many materials in nature are highly complex as they are designed for long duration. Taking nature itself as a role model means taking its complexity into account, especially when considering materials which suffer from chemical attacks and the degradation of materials. From this point of view, we create an algorithm which considers degradation processes triggered by chemical substances which depend on diffusion conditions in a finite element (FE) framework. In addition, we perform design optimisation with stress restrictions by taking evolutionary processes as a role model.
Development of a simulation model for the automatic optimization of tools for multi‐dimensional tube forming
Authors: Derr Ralf , Jung Anne , Diebels Stefan
Published: November 2019

The increasing number of vehicle components and the advancing lightweight construction in manufacturing processes increasingly require a more flexible design of the exhaust tube geometry. The use of process supplementary simulations is necessary, in order to meet these increasing requirements in the future.

The aim of this study is the development of a software tool for the simulation of multi‐dimensional tube forming processes by tube bending and tube embossing. Therefore, a graphical user interface was developed to build‐up and simulate the tube forming processes. The required material parameters for the numerical modeling were determined by means of tensile tests. The simulation models were successfully validated by comparing the numerical results with the experimental results. The influence of the workpiece and the forming tools were numerically investigated on the basis of the validated simulation models. Batch‐related tolerances could be identified as a serious source of deviations. Furthermore, experimental forming errors could be numerically reproduced and corrected by modifying the parameter settings. The tool variation increased the process knowledge and provided the basis for a subsequent optimization. The embossing structure could be optimized satisfactorily by specifying user‐defined requirements.
A formulation for the dynamic analysis of multibody systems using non‐redundant unified local velocity coordinates
Authors: Holzinger Stefan , Gerstmayr Johannes
Published: November 2019

In this paper, we present a formulation for the dynamic analysis of multibody systems using non‐redundant unified local velocity coordinates. The motivation for the present work is the result of an earlier investigation of unified local velocity coordinates of Holzinger et al. [1]. The equations of motion presented by the authors allow the description of the rigid body motion in space by local, purely translational velocity coordinates. However, the earlier investigations are limited to the description of the spatial motion of a free rigid body. Therefore, constraints are incorporated in the present paper.
Shape optimization of a bended tube minimizing particle erosion
Authors: Hohmann Raphael , Leithäuser Christian
Published: November 2019

The transport of gas‐solid suspensions in bended pipes can lead to erosion of the walls due to particle impact. In this context the numerical prediction of the erosion rate is usually based on an Eulerian flow description in combination with Lagrangian particle tracking, which however does not lend itself straightforwardly to the continuous adjoint approach of shape optimization. In order to find a pipe design, which is less prone to erosion, we therefore use a one‐way coupled Eulerian particle model. Upon formally computing the shape derivative of the resulting PDE‐constrained shape optimization problem, we minimize the erosion rate for a three‐dimensional tube bend under laminar flow conditions using a gradient descent method.
Material modeling of hyperelastic silicone adhesives considering stiffness reduction
Authors: Toups Elisabeth , Seewald Robert , Schaaf Benjamin , Reisgen Uwe , Feldmann Markus , Reese Stefanie , Simon Jaan-Willem
Published: November 2019

Predicting the hyperelastic behavior and the stiffness reduction of adhesive is essential for the economical dimensioning of load‐bearing bonds in the field of glass façade construction. The typical hyperelastic behavior can be modeled by using one of well‐known hyperelastic models. In addition, a new variable for modeling stiffness reduction was defined. A new material model based on the Ogden model for representing hyperelasticity and stiffness reduction was defined.
A juxtaposition of data driven and stochastic finite element analyses for problems with noisy material data
Authors: Korzeniowski Tim Fabian , Reppel Thomas , Weinberg Kerstin
Published: November 2019

In data driven modeling the constitutive model is replaced by a data set and therefore yields a model‐free computation. In this context the data set also can be the input for noisy material data and describe material uncertainty. This contribution presents a juxtaposition of different finite element trechniques to describe material uncertainties, namely the stochastic finite element method and a data driven finite element method.
BEM‐simulation of tubes using thin elements
Authors: Kreuzer Wolfgang , Weber Veronika
Published: November 2019

The boundary element method (BEM) is a commonly used tool in acoustics to calculate wave propagation and scattering. As for finite elements the stability of the BEM suffers if the thickness of the elements used in the discretization of the scatterer is very small. To deal with this problem special thin middle face elements have been designed. In this work we use these elements to model the acoustics of musical tubes (boomwhacker/Klangröhre), that are simple musical instruments for children. We briefly describe the integral equation for the thin elements and compare calculations using the BEM with thin elements with measurements of a tube tuned to the note ‘C’.
Proceedings in Fluid Design
Authors: Beckmann Tom , Reinke Peter , Schmidt Marcus
Published: November 2019

This work presents the process of designing a cavitating fluid for the lubricant flow in journal bearings. Hydrodynamic journal bearings are used in a wide range of technical and industrial applications because they provide low friction and minimal wear. The principal operational feature of these bearings is an eccentrically rotating shaft inside the bushing resulting in a convergent and divergent lubricating film of just a few micrometers in thickness between the shaft and the bushing. For the particular case of internal combustion engines the displacement of the shaft is transient with strong variations in eccentricity and displacement velocity. Hence, the flow inside the lubricating film is transient and three‐dimensional. Investigations of the flow inside journal bearings are technically challenging. The following geometrical and physical conditions have to be tackled: small lubricating film thickness, optical accessibility, Reynolds and cavitation similarity. The combination of these conditions requires a scaled journal bearing experiment with a special fluid that fulfills the cavitation condition. The most important component of the experimental setup is the fluid in order to create the desired flow conditions. The authors of this work have proven that a cavitating fluid can be designed to specification by applying the new approach to the cavitating Taylor‐Couette flow. The proper fluid design has to fulfill three criteria: physical compatibility, Reynolds analogy and cavitation number at the operating point. Physical compatibility stems from material specifications of the apparatus and the need to provide optical accessibility by providing identical refractive indices of fluid and housing. The fluid must be chemically compatible with acrylic glass of the apparatus preventing unwanted reactions. Laser‐optical measurements are the most suitable means to obtain significant data of the flow field inside the lubricating film. The relation of dynamic pressure at the operating point and mechanical dimensions of the apparatus defines the viscosity necessary to fulfill the Reynolds analogy. Finally, the cavitation number in relation to the combination of dynamic and static pressure provides the target vapor pressure of the special fluid. Thus, the present work describes the development of a special fluid applicable for journal bearings in model scale, which not only fulfills pressure and cavitation analogy but also features a favorable refractive index and a chemical suitability for the task. Furthermore, the work shows results of a cavitating flow in a small gap arrangement by means of the designed fluid.
A least‐squares finite element approach to model fluid‐structure interaction problems
Authors: Averweg Solveigh , Schwarz Alexander , Nisters Carina , Schröder Jörg
Published: November 2019

In this contribution an approach to model fluid‐structure interaction (FSI) problems with monolithic coupling is presented. The fluid as well as the structural domain are discretized using the least‐squares finite element method (LSFEM), whose application results in a minimization problem with symmetric positive definite systems also for non self‐adjoint operators, see e.g. [2]. In this study, the second‐order systems are reduced to first‐order systems by introducing new variables, which leads to least‐squares formulations for both domains based on the stresses and velocities as presented in e.g. [5] and [7]. A conforming discretization of the unknown fields in H1 and H(div) using Lagrange interpolation polynomials and vector‐valued Raviart‐Thomas interpolations functions, respectively, leads to the inherent fulfillment of the FSI coupling conditions. In more detail, a discretization in H1 ensures continuity of the velocity field and a discretization in H(div) results in continuity of the normal stress components at the interface.
A time‐adaptive Dirichlet‐Neumann waveform relaxation method for coupled heterogeneous heat equations
Authors: Monge Azahar , Birken Philipp
Published: November 2019

We introduce a time adaptive multirate method based on the Dirichlet‐Neumann waveform relaxation (DNWR) algorithm for the simulation of two coupled linear heat equations with strong jumps in the material coefficients across the interface. Numerical results are included to illustrate the advantages of the time adaptive approach over the multirate approach and the robustness of the multirate DNWR method with respect to its sibling, the multirate Neumann‐Neumann waveform relaxation (NNWR) method introduced in a previous work [3].
Shape Optimization in Phosphate Production
Authors: Dietrich Nicolas , Marx Thomas , Pinnau René
Published: November 2019

Phosphate as an industrial product is an essential ingredient in, e.g., agriculture and food industry. The production process is very energy consuming and takes place in high temperature melting furnaces. The costs of the productions are largely governed by the energy costs of the furnace and there is a high potential to save energy by increasing its energy efficiency. Naturally, the shape of the furnace has a high influence on its efficiency. In order to describe the temperature distribution within a furnace mathematically, a widely used model in the industry is the Rosseland approximation. We use this model and discuss the problem in the context of shape optimization.
Shape Optimization in High Temperature Processes
Authors: Marx Thomas , Dietrich Nicolas , Pinnau René
Published: November 2019

High temperature processes have a wide field of applications in industrial processes, e.g., optimal design in glass cooling or shape optimization for melting furnaces. We consider here the SP1 approximation of the Radiative Heat Equation which includes reflecting boundary effects. This leads to a PDE‐constrained shape optimization problem, where the shape of the domain is the design variable.
Comparison of the mechanical properties of milk fouling and whey protein fouling
Authors: Liu Jintian , Wiese Hanna , Augustin Wolfgang , Scholl Stephan , Böl Markus
Published: November 2019

The formation of fouling deposit is a significant problem for the dairy industry. Many experimental analyses have been carried out to explore the cleaning process using whey protein solution as a surrogate material because the main fouling components in milk are whey proteins. In view of mechanical cleaning processes, the mechanical behaviour of milk and whey protein fouling is compared using indentation and relaxation experiments and material parameters of a visco‐hyperelastic model are determined using an inverse finite element method (FEM).
An Intrusive PCE Extension of the Contour Integral Method and its Application in Electrical Engineering
Authors: Frick Eduard , Dahl David , Seifert Christian , Lindner Marko , Schuster Christian
Published: November 2019

For the study of electromagnetic waves in a 2D environment, the Helmholtz equation can be reformulated in boundary integral form by the so‐called Contour Integral Method (CIM). The influence of uncertainty in the geometry is studied via Polynomial Chaos Expansion (PCE). A distinction is made between the so‐called intrusive and non‐intrusive PCE. Both methods are applied to the CIM and compared to each other and to Monte‐Carlo simulation (MC).
Riemannian Structure and Flows for Smooth Geometric Image Labeling
Authors: Savarino Fabrizio , Schnörr Christoph
Published: November 2019

The image labeling problem can be described as assigning to each pixel a single element from a finite set of predefined labels. Recently, a smooth geometric approach for inferring such label assignments was proposed by following the Riemannian gradient flow of a given objective function on the so‐called assignment manifold. Due to the specific Riemannian structure, this results in a coupled replicator dynamic incorporating local spatial geometric averages of lifted data‐dependent distances. However, in this framework an approximation of the flow is necessary in order to arrive at explicit formulas. We discuss preliminary results of an alternative model where lifting and averaging is decoupled in the objective function so as to stay closer to established approaches and at the same time preserve the ingredients of the original approach. As a consequence the resulting flow is explicitly given, without the need for any approximation, while still exploiting the underlying Riemannian structure.
Cluster‐based network model for drag reduction mechanisms of an actuated turbulent boundary layer
Authors: Fernex Daniel , Semaan Richard , Albers Marian , Meysonnat Pascal S. , Schröder Wolfgang , Ishar Rishabh , Kaiser Eurika , Noack Bernd R.
Published: November 2019

We introduce a novel data‐driven reduced‐order modeling approach, a Cluster‐Based Network Model (CBNM). Starting point is a set of time‐resolved snapshots associated with one or multiple control laws. These snapshots are coarse‐grained into dozens of centroids using k‐means++ clustering. The dynamics is modelled in a network between these centroids comprising the transition probability and corresponding transit time. The transition parameters depend on the control law. CBNM is successfully applied to an actuated turbulent boundary layer flow. The results show that CBNM is an attractive alternative to POD models as the model is human interpretable and dynamically robust by construction.
Dual‐energy extension of the uniform‐approximation approach
Authors: Schneider Patrick , Kienzler Reinhold
Published: November 2019

In the talk an extension of the uniform‐approximation approach, that relies on the truncation of the elastic energy after a certain power of a geometric scaling factor, towards an analogous truncation of the dual energy is proposed. On the one hand, this allows for a derivation of fully defined boundary value problems including compatible displacement boundary conditions. On the other hand, the extension enables us to provide an a priori error estimate for the systematic error of the arising approximative models with respect to the exact three‐dimensional solution.

The approach is compared to the approach of a fixed kinematic assumption for the displacement field which is widely used in engineering. We show that the later approach leads in general to a more complex model for a comparable approximation accuracy so that the consistent approximation approach is to prefer.
Biomechanical simulations with dynamic muscle paths on NURBS surfaces
Authors: Penner Johann , Leyendecker Sigrid
Published: November 2019

In order to model the behaviour of muscles that work around the joints in musculoskeletal simulations, information about the muscle paths are needed. Typically, musculotendon paths, their lengths, and their force directions are modeled as the shortest connection wrapping around obstacles representing bones and adjacent tissue. In this work, the shortest path problem is described via constrained variational dynamics and is applied to a biomechanical example with muscle paths on non‐uniform rational B‐spline (NURBS) surfaces representing the wrapping obstacles. The results are compared with muscle paths from a G1‐continuous combination of geodesics [2,4,5].
Mesh adaptivity and error estimates applied to a regularized p‐Laplacian constrainted optimal control problem for multiple quantities of interest
Authors: Endtmayer Bernhard , Langer Ulrich , Neitzel Ira , Wick Thomas , Wollner Winnifried
Published: November 2019

In this work, we derive goal‐oriented error estimates and mesh adaptivity for multiple quantities of interest for optimal control problems with the regularized p‐Laplace equation as constraint. We apply the dual‐weighted residual method to the reduced formulation, and combine several quantities of interest. Finally, we present a numerical example with p = 10.
Simulation of subcritical crack propagation in hard metal microstructures
Authors: Wingender Dennis , Balzani Daniel
Published: November 2019

In order to investigate the wear mechanism in form of surface spalling in hard metals, their microstructures obtained by µCT‐scans are simulated using an extended eigenerosion framework. In order to directly exploit the voxel data from the scans, the microstructures are meshed with a voxel based algorithm which additionally leads to the generation of hanging nodes. In this contribution this simulation setup is described and numerical examples are provided, showing that the eigenerosion approach can suitably be combined with an efficient and automatized discretization using hanging nodes.
Finite‐strain thermo‐viscoplasticity for case‐hardening steels over a wide temperature range
Authors: Oppermann Philip , Denzer Ralf , Menzel Andreas
Published: November 2019

The aim of this work is the development of a thermodynamically consistent fully coupled finite‐strain thermo‐viscoplastic material model for metals. The model is based on a split of the free energy into a thermo‐elastic, a thermo‐plastic and a purely thermal part and covers nonlinear cold‐work hardening and thermal softening. Nonlinear temperature dependent effects are accounted for the elastic moduli, the plastic hardening moduli, the thermal expansion, the heat capacity and the heat conductivity. Furthermore, strain rate‐dependency of the current yield stress is realized using a temperature dependent nonlinear Perzyna‐type viscoplastic model based on an associative flow rule. The model and its parameters are fitted against experimental data for case hardening steel 16MnCr5 (1.7131).
Application of model order reduction to a finite element model of cryogenic turning
Authors: Becker Steven , Hotz Hendrik , Kirsch Benjamin , Aurich Jan C. , Müller Ralf
Published: November 2019

Metastable austenitic steels offer the opportunity of a surface layer hardening integrated in the machining process. The hardening effect is achieved by a deformation induced austenite‐martensite phase transformation, for which high mechanical loads and low temperatures are necessary, typically below room temperature. These conditions can be accomplished during cryogenic turning, allowing a phase transformation in the surface layer of the workpiece. To study the austenite‐martensite transformation behavior, information about the temperatures in the contact zone between tool and workpiece during machining is necessary, which can hardly be measured. Therefore, FE simulations of the process are utilized to calculate the transient process temperatures. In this paper the idea of projection‐based model order reduction and its implementation into the finite element program FEAP are described, allowing a solution speed‐up while maintaining accuracy of the full‐order model.
The Cattaneo Model in the context of Thermoablation of Liver Tumors
Authors: Andres Matthias , Pinnau René
Published: November 2019

Laser‐induced thermotherapy (LITT) is a medical treatment which attempts to destroy liver tumors by thermal ablation. Accurate simulation‐based predictions shall support the practitioner during the therapy. The heat transfer inside the liver is classically described by a nonlinear coupling of the bio‐heat equation and a radiative transfer model. In order to control the speed of heat propagation we consider an additional term for the second‐order time derivative of the solution and obtain a Cattaneo‐like model. For this model we investigate the problem of parameter identification in terms of PDE‐constrained optimization.
A bilinear identification‐modeling framework from time domain data
Authors: Karachalios Dimitrios S. , Gosea Ion Victor , Antoulas Athanasios C.
Published: November 2019

An ever‐increasing need for improving the accuracy includes more involved and detailed features, thus inevitably leading to larger‐scale dynamical systems [1]. To overcome this problem, efficient finite methods heavily rely on model reduction. One of the main approaches to model reduction of both linear and nonlinear systems is by means of interpolation. The Loewner framework is a direct data‐driven method able to identify and reduce models derived directly from measurements. For measured data in the frequency domain, the Loewner framework is well established in linear case [2] while it has already extended to nonlinear [6]. On the other hand in the case of time domain data, the Loewner framework was already applied for approximating linear models [3]. In this study, an algorithm which uses time domain data for nonlinear (bilinear) system reduction and identification is presented.
A CFD Model for Simulating the Electron Beam Welding of TRIP‐Matrix‐Composites
Authors: Borrmann Sebastian , Schwarze Rüdiger
Published: November 2019

The purpose of the presented model is the numerical simulation of the electron beam welding of metal matrix composites regarding heat transfer, phase change, and fluid and particle flow in the weld pool. The governing equations for the 3D, transient, incompressible heat and fluid flow are therefore extended by a phase change model and a heat source. Furthermore, Lagrangian particle tracking is used for the dispersed particle phase. The implementation of this model into OpenFOAM ensures reusability and expandability for further applications and refinements.
Optimal Dirichlet‐condition enforcement on curved boundaries for Lagrange and Hermite FEM with straight‐edged simplexes
Authors: Ruas Vitoriano
Published: November 2019

This work deals with a new method for solving boundary‐value problem posed in smooth curved two‐ or three‐dimensional domains of arbitrary shape.
Analysis of Hertzian indentation fracture using a phase field approach
Authors: Strobl Michael , Seelig Thomas
Published: November 2019

The formation and further evolution of cracks caused by the compression of a stiff indenter onto the surface of an initially defect‐free brittle solid is a fascinating problem of fracture mechanics. Its prediction, however, is still a challenging task since crack nucleation is caused by a rather weak stress concentration in the contact near‐field. The present contribution focuses on phase field simulation of indentation fracture, including crack formation at some a priori unknown location outside of the contact region and the subsequent formation of a cone crack. While the phase field method, at first glance, appears to be a promising tool to simulate the current problem we elaborate critical issues and discuss essential modifications. Finally, the indentation fracture process is simulated showing the effect of varying indenter radii on crack initiation and the influence of Poisson's ratio on the angle of cone crack propagation in good agreement with experimental findings and other theoretical studies.
Spatially Regularized Geometric Assignment for Unsupervised Label Learning on Manifolds
Authors: Zern Artjom , Zisler Matthias , Petra Stefania , Schnörr Christoph
Published: November 2019

We introduce a smooth coupled system of Riemannian flows for simultaneously learning a dictionary of manifold‐valued prototypes and assigning these prototypes to the image data in a spatially coherent way. In particular, we detail a numerical update scheme for the evolution of prototypes on the Riemannian manifold of symmetric positive definite matrices. The scheme is applied to covariance descriptors are extracted from image data in order to demonstrate our approach.
A Computational Model for Biological Tissues Considering the Influence of Injury on Growth and Remodelling
Authors: Gierig Meike , Marino Michele , Wriggers Peter
Published: November 2019

Biological tissues adapt to changed loading conditions through growth and remodelling (G&R) to reestablish a so‐called homeostatic state. On the other hand, loading conditions above their physiological limits, as during trauma or surgical procedures, cause injury and can initiate pathological G&R. Herein, a modelling approach for G&R influenced by injury is presented combining the theories of plasticity and homogenised constrained mixtures. The results show that injury has a significant impact on the G&R behaviour and thus on the accomplishment of homeostasis.
Comparing Abs‐Normal NLPs to MPECs
Authors: Hegerhorst-Schultchen Lisa C. , Kirches Christian , Steinbach Marc C.
Published: November 2019

We show that the class of unconstrained NLPs in abs‐normal form is a subclass of the class of MPECs and that the class of NLPs with general constraints in abs‐normal form is equivalent to the class of MPECs. Moreover, we compare constraint qualifications and stationarity concepts of these problem classes and observe close relations between them.
A Combined Homotopy‐Optimization Approach to Parameter Identification for Dynamical Systems
Authors: Schäfer Kai , Flaßkamp Kathrin , Fliege Jörg , Büskens Christof
Published: November 2019

When applying the single shooting approach to solve nonlinear dynamic parameter identification problems, difficulties like undesired minima can occur. To circumvent this, we apply a homotopy continuation to find global minima. In contrast to the literature, we reduce the resulting series of optimization problems to a single one which leads us to the opportunity to compute homotopy paths in a more efficient way. We demonstrate our method with the help of a numerical example.
Mixed XFEM formulation for the simulation of heterogeneities including elasto‐plastic material behaviour
Authors: Löhnert Stefan
Published: November 2019

Metal matrix composites often show large isochoric plastic deformations within the matrix material. For dominant plastic deformations this may lead to volumetric locking effects similar to locking in incompressible materials. Lower order mixed finite element formulations can alleviate this difficulty. Complex microstructures often require extensive effort to generate a mesh suitable for finite element simulations. The eXtended Finite Element Method may improve this situation by allowing for discontinuities in the displacement and/or strain field within any finite element. In this contribution a mixed XFEM formulation is presented combining the advantages of the XFEM and mixed FEM. The formulation is applied to small deformation elasto‐plasticity with linear isotropic and linear kinematic hardening. An example demonstrates its superior convergence behaviour compared to a standard XFEM formulation.
Thermo‐Chemo‐Mechanical Modeling of Cathode Particles in Lithium‐Ion Batteries
Authors: Nateghi Aref , Keip Marc-André
Published: November 2019

Lithium‐ion batteries are widely used in portable consumer electronics, power tools and electric vehicles. As the demand for Li‐ion batteries increases, a deeper understanding of the physical phenomena present in their operation becomes necessary. So far, there remain some obstacles to the wider use of Li‐ion batteries, e.g., capacity loss, self‐discharge and thermal runaway. These effects are mostly related to thermal phenomena in the battery. This underlines the importance of a deeper understanding of thermal effects in batteries. In this work, a four‐field formulation of the coupled problem of diffusion with stress generation and heat transfer in cathode particles of Li‐ion batteries is presented.
Comparison of the hybrid and multipoint‐flux method
Authors: Egger Herbert , Radu Bogdan
Published: November 2019

We compare two approaches for the efficient implementation of the mixed finite element method with applications for elliptic problems, like single phase flow, and hyperbolic problems, like the wave equations. We briefly explain the hybrid and the multipoint flux mixed finite element method (MFMFE) and conduct a comparison of the two methods in terms of efficiency.
Simulation of the flow behaviour of wood‐polymer composites in extrusion dies
Authors: Liese Fabian , Wünsch Olaf
Published: November 2019

By adding different fillers to polymers, both the mechanical and optical properties of the composite can be influenced. The addition of wood flour or fibers results in wood‐polymer composites (WPC), which are industrially processed into deckings by means of an extrusion process. As part of this project, the melt of high density polyethylen (HDPE) and fine wood flour is extruded into a square hollow profile.

By means of thermo‐rheological measurements, the shear thinning behaviour as well as the solidification behaviour of WPC at various degrees of filling levels of the wood and different temperatures could be determined. At high fill levels of wood, removal by means of a crawler belt is no longer possible due to the low elongation, so that a partial solidification of the melt prior to exiting the extrusion die by cooling is necessary. In addition to solidification, wall slip effects in the area of cooling occur as a function of shear stress, which could also be measured and modeled using the Mooney method [1]. This contribution deals wih the numerical flow field calculations of such WPC in special extrusion dies. From the thermo‐rheological data a non‐linear viscous model is created. The aims of the numerical simulations with OpenFOAM are to reduce pressure loss and create a uniform velocity field at the outlet. Different parameters such as the mass flow of the melt and the temperatur of the cooling medium are varied.
A geometrically nonlinear micromorphic damage‐plasticity model
Authors: Brepols Tim , Wulfinghoff Stephan , Reese Stefanie
Published: November 2019

The present article is concerned with a novel gradient‐extended ‘two‐surface’ damage‐plasticity model for large deformations which is based on the micromorphic approach in the sense of Forest [4]. It is discussed how the additional partial differential equation for the micromorphic (i. e., ‘nonlocal’) damage variable – which typically needs to be solved in case of gradient‐extended material models – can be derived in a natural way on the basis of an extended form of the principle of virtual work by assuming additional ‘generalized’ stresses that act within the body. As was shown recently by the authors (see [3]), the model is able to suitably counteract the well‐known mesh‐dependence problem of conventional ‘local’ models involving damage.
Simulation of Calcium Waves in a Heart Cell on Modern Multi‐Core Parallel Computing Platforms
Authors: Barajas Carlos , Kopecz Stefan , Meister Andreas , Peercy Bradford E. , Gobbert Matthias K.
Published: November 2019

Scalability of parallel computer code is a concern in applications that rely on efficient simulations. We present a demonstration of weak scalability of a hybrid MPI+OpenMP code for the numerical solution of a system of seven coupled, non‐linear, time‐dependent reaction‐diffusion equations that model calcium induced calcium release in a heart cell. The results demonstrate that care needs to be taken in the implementation of the OpenMP pragmas to achieve weak scalability within a shared‐memory node and that MPI is capable to provide strong scalability across multiple nodes in a distributed‐memory cluster.
On the origin of passive rotation in rotational joints, and how to calculate it
Authors: Du Shucen , Schlattmann Josef , Schulz Stefan , Seibel Arthur
Published: November 2019

In this paper, a computation method for the output shaft's rotation of a passive rotational joint, especially of one that is deployed on a parallel mechanism, is investigated. As an alternative to typical geometric or screw theory methods, we propose a new approach that is based on the comparison between any passive rotational joint with a reference spherical joint. As examples, we apply our method to a universal joint and a novel double joint whose passive rotation is difficult to calculate with traditional methods.
Remarks on pure and simple shear
Authors: Voss Jendrik , Thiel Christian , Martin Robert J. , Neff Patrizio
Published: November 2019

In a 2012 article in the International Journal of Non‐Linear Mechanics, Destrade et al. showed that for nonlinear elastic materials satisfying Truesdell's so‐called empirical inequalities, the deformation corresponding to a Cauchy pure shear stress is not a simple shear. Similar results can be found in a 2011 article of L. A. Mihai and A. Goriely. We confirm their results under weakened assumptions and consider the case of a shear load, i.e. a Biot pure shear stress. In addition, conditions under which Cauchy pure shear stresses correspond to (idealized) pure shear stretch tensors are stated and a new notion of idealized finite simple shear is introduced, showing that for certain classes of nonlinear materials, the results by Destrade et al. can be simplified considerably.
Bouc hysteresis without an elastic restoring force under white noise excitation using the beta distribution
Authors: Kasess Christian H. , Waubke Holger
Published: November 2019

The Bouc model comprises three coupled first‐order differential equations which describe the behavior of hysteretic materials. Closure methods have been shown to yield good approximations of the probability density of the state variables under white noise excitation. Previously, a new closure approach for hysteretic softening behavior was introduced, utilizing the beta distribution together with a non‐linear mapping using the inverse hyperbolic tangent. This allows to properly model the finite support of the distribution of the hysteretic force. In the current work, this beta closure approach was applied to single‐degree‐of‐freedom‐systems under stationary white noise excitation lacking, however, an elastic restoring force. Thus, no stationary state is reached. Although the results show a good agreement with Monte‐Carlo simulations there are still deviations in certain higher order moments of the displacement and the velocity depending on the noise strength.