bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermo‐mechanical modelling and finite element analysis of self‐piercing riveting processes
Authors: Nahrmann Marvin , Matzenmiller Anton
Published: December 2018

In this contribution, a thermo‐mechanical finite element analysis of the self‐piercing riveting process of two steel sheets is carried out taking into account the conversion of plastic work into heat. Thereby, a user defined constitutive model recently proposed by BRÖCKER and MATZENMILLER is applied considering the highly temperature and rate dependent characteristics of metals. All constitutive parameters are identified with test data of the microalloyed steel HX340LAD typically used for car body structures. The numerical results of the self‐piercing riveting process are compared to the according test data for model validation by means of the final joint geometry and the setting force.
Improving the Performance of Numerical Algorithms for the Bethe‐Salpeter Eigenvalue Problem
Authors: Benner Peter , Marek Andreas , Penke Carolin
Published: December 2018

The Bethe‐Salpeter eigenvalue problem arises in the computation of the electronic structure of many‐body physical systems. The resulting matrix is complex, admits a certain block structure and can become extremely large. This raises the need for structure‐preserving algorithms running in parallel on high performance compute clusters. In this paper we examine how a recently proposed direct method given in the BSEPACK library can be improved using eigenvalue solvers from the ELPA library. For large matrices a runtime reduction of up to 80% is achieved.
Extended Simulations of the Roll Bonding Process
Authors: Klinge Sandra , Aygün Serhat , Bambach Markus
Published: December 2018

Roll bonding is a joining‐by‐forming process in which two or more layers of different metals are passed through a pair of flat rolls. Under the high pressure, a permanent bond between the metals is generated by plastic deformation. The main factors influencing this process and the creation of bond strength are the size of the surface area and the normal pressure in the interface. In order to numerically predict the bond strength the FE implementation of a contact algorithm is performed. Simultaneously, the physical mechanisms typical of plastic deformation are taken into consideration. The focus particularly lies on the micro‐mechanical modeling of strain hardening by dislocation slip. A first study is given on the effects of the chemical impurities on the dislocation density and motion.
Near‐critical turbulent open‐channel flow over wavy bottom
Authors: Müllner Markus
Published: December 2018

Steady two‐dimensional turbulent free‐surface flow in a channel with mild baseline slope is considered. The shape of the channel bottom is assumed to be undular with a very small amplitude. Asymptotic expansions for large Reynolds numbers and Froude numbers slightly above the critical value 1, respectively, give for the surface elevation a differential equation of KdV‐type, with the additional terms representing turbulent dissipation and forcing due to the wavy bottom, respectively. No turbulence modelling is required. This asymptotic approach was used in [1] to describe stationary solitary waves in a channel with plain bottom and small variations in the bottom friction coefficient. It was shown recently [2,3] that there exist stationary single‐wave solutions of a different kind that are characterized by smaller wave amplitudes. In [4], both kinds of single stationary waves above single obstacles (bumps, ramps) are investigated theoretically and experimentally. In this paper, stationary space‐periodic surface waves for channel bottoms with undular shape are studied. First, a one‐parametric family of exact solutions for particular bottom shapes is derived. Remarkably, these particular solutions exist only in a narrow parameter range. The solutions are reproduced with a numerical solver to verify that the solver gives correct results. Secondly, a different type of asymptotic expansion is performed in order to describe solutions characterized by smaller wave amplitudes. The resulting linear differential equation is solved numerically. Both solutions are briefly discussed.
Pareto Front Interpolation Based on Parametric Sensitivity Analysis in a Bi‐Objective Setting
Authors: Berger Arne , Knauer Matthias , Büskens Christof
Published: December 2018

This paper shows how a discrete approximation of a Pareto front can be refined with polynomial interpolation. For this we exploit the information given by the discrete samples of the Pareto front and in addition we use parametric sensitivity information from these samples. The pararmetric sensitivities are afterwards used to ensure feasibility of the obtained interpolated solutions by applying an iterative self correction algorithm. Results are shown for an bi‐objective example.
Numerical material testing based on statistically similar representative volume elements for discontinuous fiber composites
Authors: Sasagawa Takashi , Tanaka Masato , Omote Ryuji , Balzani Daniel
Published: December 2018

A computational method is proposed for the construction of statistically similar representative volume elements (SSRVEs) for discontinuous fiber composites (DFCs) in order to efficiently calculate material properties based on computational homogenization. The SSRVE is obtained by solving an optimization problem which minimizes differences between the power spectral density of a real target microstructure and the SSRVE. The target microstructure is obtained by means of computed tomography scanning of a DFC plate. As a result of a comparative study, the mechanical behavior of the SSRVE turns out to agree with that of the target microstructure. However, the SSRVE reduces extremely the computational costs of finite element analyses to derive macroscopic material properties of DFCs.
Staggered grid discretizations on Lie groups with applications in beam and shell theory
Authors: Hante Stefan , Arnold Martin
Published: December 2018

We will discuss staggered grid space discretizations for micropolar Cosserat models with nonlinear configuration spaces, that have Lie group structure. The discretization scheme is applied at the level of the variational principle, has second order truncation error and uses a staggered grid, where the spatial derivatives are discretized inbetween the discretization points of the material configuration.
An intelligent meta‐element for linear elastic continua
Authors: Koeppe Arnd , Bamer Franz , Markert Bernd
Published: December 2018

Large numbers of nodes and nonlinearities make the numerical solution of finite element models computationally expensive. We introduce “intelligent” elements for linear elastic continua, which use neural networks to reduce the number of nodes, and demonstrate their efficiency on two benchmark examples. It is shown, that models with “intelligent” meta‐elements accurately solve the boundary value problem and require a smaller number of nodes than conventional finite element models.
Variational Integrators for Parameter Identification of Mechanical Systems
Authors: Flaßkamp Kathrin , Schäfer Kai , Büskens Christof
Published: December 2018

Numerical methods for parameter identification of dynamical systems are based on matching model outputs to measurements. Computing the model output requires numerical integration techniques, though. In this contribution, we study the role of integration methods for mechanical systems. Since mechanical systems have characteristic properties, using structure‐preserving integration methods suggests itself. First and second order methods are compared in the case study of a damped pendulum.
Lattice Boltzmann method applied to antiplane shear loading of a stationary crack
Authors: Reinirkens Thomas , Müller Ralf , Kuhn Charlotte
Published: December 2018

In this work, the dynamic behavior of linear elastic solids under antiplane shear deformation is studied by the Lattice Boltzmann method (LBM). The governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. We use the approach developed by Guangwu as starting point to solve this problem numerically. The numerical performance of the lattice Boltzmann scheme is tested for a stationary crack which can be compared to an analytical solution. Furthermore the performance of the lattice Boltzmann simulations are compared to classical Finite Element Method (FEM) computations with regard to calculation time and accuracy. Finally the stability with respect to the relaxation parameter is studied.
Variational Homogenization for Phase‐Field Modeling of Micro‐Magneto‐Mechanics at Finite Deformations
Authors: Vallicotti Daniel , Sridhar Ashish , Keip Marc‐André
Published: December 2018

Composite materials of soft polymers with embedded ferromagnetic particles, so‐called magnetorheological elastomers (MRE), are advantageous due to the possible large deformations under moderate applied magnetic fields. In order to understand the underlying physical phenomena a multiscale view on microscopic magnetic domain evolution and its effect on the overall macroscopic response is of utmost importance. We propose a multiscale variational framework for micro‐magneto‐mechanical response at large deformations embedded into a scale‐bridging scenario by using homogenization techniques in order to define the macroscopic overall response of MREs. Starting point is a rate‐type saddle‐point variational principle at microscale yielding the Euler‐Lagrange equations including the Landau‐Lifshitz equation for the magnetization [3]. Particular challenges lie in the algorithmic treatment of the related physical unity constraint of the magnetization director and in the link of the gradient‐type continuum description of the micro‐structure to a local magneto‐mechanical macro‐continuum. A staggered solution scheme on the microscale as proposed in [2] together with a macroscopic driving routine related to [1] offers the coupled two‐scale algorithmic solution. A numerical example demonstrates the capabilities of the framework and shows the effect of particle interactions based on evolving magnetic domains on the overall macroscopic response.
Constitutive modelling of hyperelastic rubber‐like materials accounting for damage
Authors: Toups Elisabeth , Reese Stefanie , Simon Jaan‐Willem
Published: December 2018

Adhesives are used in numerous applications such as in the automotive industry, packaging industry, civil engineering, and many others. The use of multi‐side bonded joints becomes increasingly common in glass‐façade structures instead of bolted point fixings, inter alia, for aesthetic reasons. For the simulation of glass‐façade components, it is essential to investigate constitutive models which ensure a representation of rubber‐like material behaviour. Several hyperelastic material models are available in the literature, but most of them are not suitable to represent large deformations, damage (i.e. Mullins‐Effect), and multiaxial stress states all in one. Hence, the main goal of the present work is to develop a material model which exhibits the mentioned properties.
Simulation of residual stresses and their impact on geometrical accuracy in incremental sheet metal forming
Authors: Maqbool Fawad , Bambach Markus
Published: December 2018

The current study presents the influence of the process parameters on residual stresses and geometrical accuracy in single point incremental forming (SPIF). In SPIF, a sheet metal is formed by the continuous localized deformation of a hemispherical tool. In this regard, pyramidal parts from an aluminum alloy are incrementally formed by varying the process parameters. Small strips are cut from the side walls of these pyramids and the resulting curvature of the strips is measured and compared. The bore‐hole‐drilling method is used to measure the residual stress state. Further, two different numerical models employing isotropic and mixed hardening rules are calibrated based on the residual stresses. The model with mixed hardening predicts better results. This validated numerical model is used to simulate the geometric deviation upon trimming. The resulting curvature of the trimmed strips from the numerical simulations is compared to the curvature of the experimental strips. A good agreement is found. Hence, the developed model can be used to accurately simulate the residual stresses and in turn the trimmed geometry after SPIF.
Asymptotic properties of high‐speed waves in atomic chains
Authors: Herrmann Michael , Matthies Karsten
Published: December 2018

We summarize some recent asymptotic results on the appoximation and the stability of high‐speed waves in FPUT chains.
An Anisotropic Damage‐Mode Based Constitutive Model for Fibre‐Reinforced Polymer Composites
Authors: Chatiri Madhukar , Matzenmiller Anton
Published: December 2018

This contribution presents a three dimensional constitutive model for anisotropic damage to describe the onset and propagation of ply failure mechanisms in unidirectional fiber reinforced laminated composites. The primary objective of the work focuses on the three dimensional relationship between damage of the material and the effective elastic properties for the purpose of stress analysis of composite structures. Damage initiation criteria are based on Puck failure criterion for first ply failure and progressive micro crack propagation is based on the idea of continuum damage evolution.
A micromechanical model of filled elastomers based on the directional hydrodynamic strain amplification factor
Authors: Darabi Ehsan , Itskov Mikhail , Klüppel Manfred
Published: December 2018

A constitutive model for filled elastomers is proposed based on the combination of the continuum damage [1] and the dynamic flocculation [2] framework. Damage takes place in both the network rubbery matrix and inside the filler aggregates. Accordingly, the probability density functions of the number of segments and the filler size distribution in all spatial directions evolve with deformation, which causes stress softening, the Mullins effect and induced anisotropy. Multiple breakage and reaggregation of filler clusters with different sizes in various spatial directions are the main sources of the directional hydrodynamic strain amplification. The model includes a few number of physically motivated material constants characterizing the average filler cluster dimension, filler‐filler and filler‐matrix interaction properties.
Micromechanical Modeling of a Generator Stator Electrical Insulation System
Authors: Nguyen Thank Thank , Wulfinghoff Stephan , Reese Stefanie
Published: December 2018

A gradient‐extended damage theory is shortly presented. The focus is on the internal thermodynamic forces and their extension to gradient‐extended models. This continuum mechanical framework is used for an application to an anisotropic damage model with a 2nd order damage tensor.
Combining Finite Elements and Random Fields to Quantify Uncertainty in a Multi‐phase Structural Analysis
Authors: Henning Carla , Herbrandt Swetlana , Ickstadt Katja , Ricken Tim
Published: December 2018

For a wide range of mechanical application fields, computational analyses are already indispensable due to their advanced impact on engineering developments. They provide a lot of information about the functioning and structural response of an arbitrary structure and the interaction with its surrounding. Nevertheless, despite preliminary investigations or the knowledge about manufacturing process of structures, assumptions of geometrical or material properties are often sources of uncertainties. These can be distinguished into aleatoric (e.g. natural scattering of properties) and epistemic (e.g. accuracy of the numerical approximation) uncertainties. Although measuring devices or process workflows are continuously improved, there always remains a residual risk. In order to provide and improve decision‐making tools for end users, the priority program SPP 1886 has been installed by the DFG with the focus on polymorphic uncertainty quantification. The present subproject, which is part of the SPP 1886 (sp12), is focused on fluid saturated soil and earth structures and their multiple uncertainty sources.

The very complex micro‐structural consolidation mechanism of soil requires a suitable numerical description. For the strongly coupled fluid‐solid response behavior, the Theory of Porous Media (TPM) will be used, a macroscopic homogenization approach based on the mixture theory restricted by the concept of volume fraction. In the framework of the Finite Element Method (FEM), arbitrary Boundary Value Problems (BVP) can be investigated. Uncertainty modelling takes place on the stochastic level by introducing random fields with a defined correlation structure for the generation of model initial material parameters. By generating many random field realizations for a FEM material parameter, we receive various FEM outputs for selected scenarios of the stated BVP. These results can be used to identify typical output scenarios, which allows to identify critical material parameter combinations which may cause instabilities.
Localization studies for ground states of the Gross‐Pitaevskii equation
Authors: Altmann Robert , Peterseim Daniel , Varga Dora
Published: December 2018

For oscillatory high‐amplitude potentials it is known that the linear Schrödinger operator leads to exponentially localized ground states. This localization result can be quantified explicitly in terms of geometric parameters and the degree of disorder within the potential. In the present paper we study the influence of the amplitude and the importance of the periodicity in the nonlinear setting of the Gross‐Pitaevskii equation which models ultracold bosonic gases.
Global and goal‐oriented reanalysis in nonlinear structural mechanics
Authors: Materna Daniel
Published: December 2018

Reanalysis methods can be used in order to reduce the overall computational cost in numerical simulation. In this contribution an approach for global and goal‐oriented nonlinear reanalysis based on residual increment approximations (RIA) is presented. The method requires only the evaluation of residual vectors, which can be done very fast and efficient. Moreover, the results are improved by using a rational approximation method. The approach is general and can be applied to linear and nonlinear problems with different kind of design modifications. Furthermore, the proposed method is very efficient and easily to implement in existing finite element programs, because no derivatives with respect to the design variables are necessary.
Approximation of Hermitian Matrices by Positive Semidefinite Matrices using Modified Cholesky Decompositions
Authors: Reimer Joscha
Published: December 2018

A new algorithm to approximate Hermitian matrices by positive semidefinite matrices based on modified Cholesky decompositions is presented. The approximation error and the condition number of the approximation can be controlled by parameters of the algorithm. The algorithm tries to minimize the approximation error in the Frobenius norm. It has no significant runtime and memory overhead compared to the computation of an unmodified Cholesky decomposition. Sparsity and positive diagonal entries can be preserved. A Cholesky decomposition of the approximation matrix is calculated as a byproduct.
Multi‐field formulation of large deformation ductile fracture
Authors: Dittmann Maik , Hesch Christian , Schulte Jonathan , Aldakheel Fadi
Published: December 2018

In the present contribution we focus on a novel computational framework for the simulation of ductile fracture in elastoplastic solids. In particular, a fully non‐linear formulation of gradient plasticity is applied together with a higher order phase‐field approach to fracture to account for large elastic and plastic deformations along with three dimensional crack propagation. The proposed formulation is based on a multiplicative decomposition of the deformation gradient into elastic and plastic contributions and a subsequent multiplicative decomposition of the elastic part into a fracture sensitive and a fracture insensitive contribution, see [1]. Postulating that fracture requires a local state of tensile/shear deformation, the latter decomposition is used to formulate the isochoric and tensile contributions to the elastic strain energy, whereas the compressive contribution remains unaffected by the crack phase‐field and vice versa. The modification of the Griffith brittle fracture theory to ductile fracture is most crucial and has to be adjusted carefully. Within our framework, this adaptation is considered as dependency of the critical fracture energy density by the equivalent plastic strain. Concerning the elastic/plastic decomposition, we assume an isochoric plastic flow which requires special attention for the update procedure of the plastic deformation. To be specific, we apply an exponential time integration scheme such that we preserve the deviatoric state of the plastic deformation and obtain a correct evaluation of the phase‐field driving force. Eventually, a number of numerical examples will demonstrate the accuracy and capability of the proposed multi‐field approach to ductile fracture.
Active control of foams by physically based destruction mechanisms
Authors: McHardy Christopher , Thünnesen Julian , Horneber Tobias , Kostova Jordanka , Hussein Mohamed A. , Delgado Antonio , Rauh Cornelia
Published: December 2018

Foams may be undesired in technical processes and need, thus, to be actively controlled. In food science engineering it is often not possible to apply chemical measures due to the required purity of the processed products. To overcome this challenge it is necessary to apply physically based foam destruction mechanisms. The present contribution deals with the prediction of foamability and the application of acoustical foam destruction from an experimental point of view. The results show that it is possible to classify the foamability of different fluids by a correlation of dimensionless numbers containing purely physico‐chemical properties (i.e. density, surface tension, viscosity). The foam stability is a consequence of the net balance of the foam generation and the foam decay. The respective time scales may be influenced by the process conditions, the fluid properties, and the selected physically based destruction mechanism. In the case of resonance excitation of foam bubbles by acoustic waves of defined frequencies selective foam destruction can be achieved. The bubbles in the foam start to oscillate and absorb energy depending on the bubble size, fluid properties, and ultrasound frequency. The resulting bubble breakdown leads to a shortening of the time scales of the foam decay.
Parallel solution, adaptivity, computational convergence, and open‐source code of 2d and 3d pressurized phase‐field fracture problems
Authors: Heister Timo , Wick Thomas
Published: December 2018

We present a scalable, parallel implementation of a solver for the solution of a phase‐field model for quasi‐static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show optimal scaling of the linear solver based on algebraic multigrid, and convergence of the phase‐field model towards exact values of functionals of interests such as the crack opening displacement or the total crack volume. In contrast to uniform refinement, adaptive mesh refinement allows us to recover optimal convergence rates for the non‐smooth solutions encountered in typical test problems. We also present numerical studies of the influence of the finite domain size on functional evaluations used to approximate the infinite domain.
A discrete, two‐dimensional frictional contact model for dynamic contact between viscoelastic materials and rough counterparts
Authors: Schulte Frank , Sextro Walter
Published: December 2018

Friction between a viscoelastic material and a rough surface occurs in many technical applications, e. g. windshield wiper, rubber gaskets or the tire‐road contact. For the investigation of friction phenomena a detailed frictional contact model is necessary. The friction of viscoelastic materials is divided into the two main effects hysteresis friction and adhesion friction. Multiple influence factors on the friction behaviour are known, e. g. material properties of the contact partners, normal force, excitation frequency through the counterpart, as well as temperature. Due to the frictional forces a system is significantly influenced in its vibrational properties. For the simulation of the complex friction processes with viscoelastic materials, a two‐dimensional friction contact model with the assumption of an isotropic roughness has been developed. The model consists of a rough rigid and a rough viscoelastic layer. The rough rigid layer represents a measured roughness profile. Due to the low stiffness of the viscoelastic material, the counter body can be assumed to be rigid. The viscoelastic layer consists of a number of point‐masses with generalised Maxwell‐models and represents the viscoelastic material. By this model the normal and tangential contact can be simulated dynamically. Effects such as changing the contact status during the friction process are taken into account. A stiffening of the viscoelastic material and thus a lower real contact surface at higher excitation frequencies or low temperatures can be shown with the model. This is especially important for the calculation of adhesion friction, as it depends directly on the actual contact area.
Stability Issues in Hardware‐in‐the‐Loop Tests of Flexible Components
Authors: Bartl Andreas , Insam Christina , Rixen Daniel J.
Published: December 2018

The well‐known Hardware‐in‐the‐Loop (HiL) paradigm can be applied to numerous engineering problems to test components of complex systems and their dynamical effects under realistic boundary conditions. The system is split into a virtual component and a physical testbed. Coupling both with a control system makes it possible to replicate the full system's dynamics. However, the system may exhibit stability problems, depending on dead times, actuator dynamics and dynamical properties of the test specimen. In this contribution, the properties of a simple lumped mass system and their effects on stabilty and accuracy are investigated.
Data‐driven approximation methods applied to non‐rational functions
Authors: Karachalios Dimitrios S. , Gosea Ion Victor , Antoulas Athanasios C.
Published: December 2018

In this study, four data‐driven interpolation‐based methods are compared. The aim is to construct reduced‐order models for which the corresponding rational transfer function matches the original non‐rational one at selected interpolation points. The primary method of this study is the Loewner framework [2] which addresses this problem in a natural and direct way. The other methods that were studied, vector fitting (VF) [5], and adaptive Antoulas‐Anderson (AAA) [4], are instead based on an iterative and adaptive selection procedure. In order to present the adaptive selection as a feature in the Loewner framework and to reduce the time complexity at the same time, we introduced a Loewner CUR method based on the cross approximation algorithm [6,7]. The performance of the above methods is tested by a classical example in approximation theory: the inverse of the Bessel function of the first kind.
Optimal Power Flow Subject to Non‐Gaussian Stochastic Uncertainties: An L2‐based Approach
Authors: Mühlpfordt Tillmann , Faulwasser Timm , Hagenmeyer Veit
Published: December 2018

The optimal power flow (OPF) problem—i.e., the task to minimize power system operation costs while maintaining technical and network limitations—is key for the operational planning of power systems. The influx of inherently volatile renewable energy sources calls for methods that allow to consider stochasticity directly in the OPF problem. Modeling uncertainties as second‐order continuous random variables, the OPF problem subject to stochastic uncertainties can be posed as an infinite‐dimensional L2‐problem. A tractable and exact reformulation thereof can be obtained using polynomial chaos expansion, under mild assumptions. Polynomial chaos as such is a Hilbert space series expansion for random variables that is frequently employed for uncertainty propagation and uncertainty quantification. Polynomial chaos offers several advantages for OPF subject to stochastic uncertainties. For example, multivariate non‐Gaussian uncertainties can be considered straightforwardly. Also, the solutions from polynomial chaos are effectively feedback laws in terms of the realizations of the uncertainty that are determined in a single numerical run.
Finite element formulation of elastoplastic structures by using the symplectic Brezis‐Ekeland‐Nayroles principle
Authors: Shirafkan Nima , Nguyen An Danh , Stoffel Marcus , Markert Bernd
Published: December 2018

In this contribution, we present a finite element formulation to study elastoplastic structures by using the symplectic Brezis‐Ekeland‐Nayroles (BEN) principle. The approach that provides a minimum principle for the whole trajectories is suitable for dissipative systems dealing with non‐smooth dissipation cases, such as collision, surface friction, viscosity, plasticity, fracture and damage. To derive the variational formulation, the Legendre‐Fenchel transform is performed to establish the null minimisation problem of the power balance. The formalism is specialised to the small strain plasticity and is illustrated by solving a plane strain problem subjected to tensile force. The continuum is discretised with mixed finite element method and implemented into Finite Element Analysis Program (FEAP).
Modeling of Ductile Fracture by a Phase Field Approach
Authors: Müller Ralf , Noll Timo , Kuhn Charlotte
Published: December 2018

A phase field model for ductile fracture with linear isotropic hardening is proposed. The chosen coupling between the fracture field and the elastic‐plastic material law is chosen such that a monolithic iteration scheme to solve the discretized partial differential equations for the evolution of the fracture field and for the mechanical field is feasible. 3D examples of ductile fracture are considered.
Simulation of a hollow profile extrusion process for a semicrystalline polymer
Authors: Descher Stefan , Wünsch Olaf
Published: December 2018

In this contribution the flow inside a simplified device for profile extrusion is investigated. Focus of this work is the cooling rate dependent crystallization model describing the latent heat release and state of solidification. The flow behavior is described using the exponential form of the Phan‐Thien Tanner model. Calculations are performed using OpenFOAM.
Numerical = periodic homogenization
Authors: Peterseim Daniel , Varga Dora
Published: December 2018

In our work, we try to bridge the existing theory of classical homogenization and the practical methods in numerical homogenization. We suggest an effective coefficient, which stems from the LOD method and which is based on a triangulation of the underlying domain. It turns out that in the case the diffusion coefficient has periodic structure and for a suitable choice of the mesh, the suggested coefficient coincides with the homogenized coefficient from classical homogenization.
Investigations in the field of material mechanics using strain gages
Authors: Lehmann Thomas , Stockmann Martin , Ihlemann Jörn
Published: December 2018

In this contribution, investigations of the stress‐strain behavior of different metals using strain gage technique are presented. The measurement of strains using strain gages provides high measuring accuracy. In case of large deformations, the nonlinearity of the resistance‐strain‐relation, including elastic and plastic strain of the gage grid material, has to be considered. Moreover, for the detection of large deformations, high‐elongation strain gages and special bonding adhesives are used. Furthermore, at larger resistance changes the nonlinearity of the Wheatstone bridge has to be taken into account. As an example, the stress‐strain behavior of the steel 50CrV4 with 3 different process states in the small deformation range during tensile tests is demonstrated. The differences of the resulting stress‐strain curves of the material in the different process states are analyzed. Additionally, specimens of the aluminum alloy EN AW‐2024 are investigated in a large deformation range using tensile tests. Therein, the strain transmission enabled by the bonding is in the special focus. Furthermore, results of the large deformation tests are compared to the strain measurement using Digital Image Correlation.
Computational stability analysis of magnetorheological elastomers across scales
Authors: Keip Marc‐André , Polukhov Elten
Published: December 2018

The present contribution discusses the computational multiscale stability analysis of magnetorheological elastomers (MRE) across multiple length scales. The effective properties of the MRE are determined by means of computational homogenization over representative volume elements (RVE). Localization‐type macroscopic instabilities are detected by checking the strong‐ellipticity condition of homogenized moduli. At micro‐level, bifurcation‐type instabilities are treated by means of a finite‐element based Bloch‐Floquet wave analysis. The latter allows to find changed periodicities of microstructures as well as critical macroscopic loading points. Some representative numerical examples demonstrate various aspects of instabilities occurring in MREs.
Stacking Sequence Optimization of Multilayer Composite Materials
Authors: Loske Simon , Barthold Franz‐Joseph
Published: December 2018

The application of composite materials in various types of devices has increased steadily in the past decades. Hence, it is worth investigating into the structural behavior of these materials. The optimization of stacking sequences in multilayer composite materials opens a large field of improvements in industrial applications of composite materials. The center of investigation is set on fiber reinforced laminate plies, which are examined in the case of linear anisotropic theory of elasticity and applied to an isoparametric shell element formulation. For these mechanical systems, the modeling approach using lamination parameters is consulted. Under application of these lamination parameters, an optimization problem is formulated which uses an optimization procedure based on the SQP algorithm that optimizes the material properties of laminates to maximize the stiffness of the considered structure. The material properties obtained by the optimization of the lamination parameters are converted into possible stacking sequences for laminates by using simplified approaches.
Influence of friction‐induced heating on the dynamic behaviour of rotors supported by journal bearings
Authors: Irmscher Cornelius , Nitzschke Steffen , Daniel Christian , Woschke Elmar
Published: December 2018

Different oil‐film‐induced instabilities have to be accounted for when designing rotor systems supported by hydrodynamic bearings. Because the system's behaviour is strongly dependent on the thermal state, this contribution presents an approach for calculating the thermo‐hydrodynamic behaviour of a bearing‐rotor‐system. It incorporates a solution of the three‐dimensional energy equation for the fluid film and accounts for heat conduction through the surrounding parts of the bearing. The simulation model is validated with the help of experimental data and improvements are pointed out compared to an isothermal approach.
Mesh Bias for the Eigenerosion Approach
Authors: Qinami Aurel , Kaliske Michael
Published: December 2018

In fracture mechanics, having the right crack path is a necessary condition for achieving reliable results. On the other hand, a discretized continuum is unable to represent a random crack path perfectly. Thus, challenges lie ahead on the accuracy of the numerical representation of this crack. Albeit the eigenfracture scheme has been well established in the recent years, different simulation results have shown some dependencies of the crack path on the mesh orientation, particularly when dealing with unstructured meshes. An r‐adaptive mesh refinement technique is introduced in this work, which circumvents possible mesh bias. In this regard, eroded finite elements are adaptively aligned in the direction of configurational forces calculated at the crack tip. Investigating the bounds of the eigenerosion scheme related to meshing and the introduction of possible improvements contribute to avoiding mesh induced anisotropy and further consolidate the approach.
The effect of the medium‐range configuration on the atomistic fracture behaviour of vitreous silica
Authors: Ebrahem Firaz , Bamer Franz , Markert Bernd
Published: December 2018

Using molecular dynamics simulations, we prepare vitreous silica by quenching molten silica to ambient temperature. Varying the quenching rate, we show that the latter barely influences the short‐range order, whereas the medium‐range configuration is significantly affected. We subject the prepared silica specimens to tension until fracture occurs and demonstrate the effect on the material behaviour. We evaluate the medium‐range configuration in terms of the ring statics of the glass network structure. Linking the ring statistics with the deformation and fracture behaviour of vitreous silica, we provide a topologically motivated explanation of the material behaviour.
Chemical active porous media with internal mass exchange
Authors: Sauerwein Malte , Steeb Holger
Published: December 2018

The aim of this contribution is to model a multiphasic material subjected to internal phase transition. The material is composed of a porous matrix, while the pore space is simultaneously filled with an aqueous pore fluid and a visco‐elastic gel. The latter one is made of a granulate of cross‐linked polyelectrolytes, also known as superabsorbent polymers (SAPs). Depending on the pore fluid chemistry, e. g. the concentration of mobile ions, the polymer phase absorbs water from the pore fluid and transforms to a hydrogel. Since the hydro‐mechanical properties of the overall mixture, e. g. the intrinsic permeability, depends on the phase transition process in the void space, a reliable constitutive modeling for the inter‐phase mass exchange has been carried out. In addition, comparison with experimental data shows that the derived continuum model is able to mimic phase transition processes for different NaCl concentrations in the pore liquid.
Computational modelling of fretting wear of Ti‐6Al‐4V incorporating cyclic plastic deformations and the debris evolution
Authors: Zhang Le , Ma Songyun , Markert Bernd
Published: December 2018

In the present work, a new fretting wear model taking account of the dynamic evolution of the debris layer is proposed to predict the wear profile under gross sliding conditions. The dynamic evolution of the debris layer is described by an exponential function of the debris thickness. A multi‐linear kinematic hardening model is employed to describe the cyclic plastic deformation of Ti‐6Al‐4V. The ejection rate of debris is computed to account for the accumulation of the debris thickness. Different wear configurations are used to validate the predictive ability of the proposed wear model. The simulation results show that the proposed approach provides a reasonable prediction of wear profiles in different wear configurations.
Partitioned simulation of multi‐field problems – efficient and robust coupling of fluids and structures
Authors: Radtke Lars , Lampe Tobias , Abdel‐Maksoud Moustafa , Düster Alexander
Published: December 2018

Strongly coupled multifield problems arise in various engineering applications. Fluid‐structure interaction problems are one of the most prominent examples, especially in maritime applications. Choosing a partitioned solution approach allows to reuse existing software that was specialized to solve the underlying structural and fluid dynamics subproblems. In this work, the general partitioned solution approach is applied to investigate the hydrodynamics around an elastic marine‐propeller. The software library comana is used to steer the solution process. It allows to couple a boundary element solver for the fluid subproblem with a finite element solver for the structural subproblem. It is shown that novel convergence acceleration methods ensure a stable and efficient simulation for different coupling algorithms.
The effect of the collagen fibrils network on the damage behaviour of articular cartilage: a computational study
Authors: Liu Dongxu , Ma Songyun , Stoffel Marcus , Markert Bernd
Published: December 2018

Collagen fibrils are the main composition of articular cartilage. The aim of this work is to study the influence of the collagen network on the damage behaviour of articular cartilage by employing a multiscale computation approach. For this purpose, a visco‐hyperelastic damage model based on the finite strain theory is proposed to describe the damage process of collagen fibrils. Stress and damage distributions are investigated to determine the influence of the fibril morphology on the cartilage damage. The computation results reveal that the location and magnitude of the damage in cartilage are strongly dependent on the orientation, distribution and the ratio between the primary and secondary level of the collagen fibrils.
Numerical Analysis for Time‐Dependent Electromagnetic Field Control
Authors: Bommer Vera , Yousept Irwin
Published: December 2018

An optimal control problem of the full time‐dependent Maxwell equations and its numerical approximation are presented. A mixed finite element discretization in space and a Crank‐Nicolson scheme for the time‐dependent Maxwell equation lead to a discretized optimal control problem. A numerical example illustrates our approach.
Smoothed Particle Hydrodynamics model of poroelasticity‐fluid coupling
Authors: Osorno Maria , Steeb Holger
Published: December 2018

Analysis of hydraulic fracturing is highly relevant in the exploration and production of geothermal energy. The simulation of fluid‐filled fractures in porous media requires to model the coupling between a fracture saturated with a compressible fluid and a surrounding (fluid‐saturated) poroelastic rock. A numerical investigation of hydraulical fracturing in poroelastic media includes the treatment of evolving fractures and possible large deformations. The use of classical mesh‐based methods in these cases implies computationally expensive geometrical meshing and remeshing pre‐processing. Furthermore, employing mesh‐based methods may entail other error sources, such as mesh distortions and fracture mesh‐alignment. To overcome these difficulties, we use the meshless method Smoothed Particle Hydrodynamics (SPH). We apply the proposed model to low‐ratio fractures with rough surfaces and analyze the effect the fractures asperities.
Control design for a 2 ⊗ 2 hyperbolic system with application to preferential crystallization
Authors: Zuyev Alexander , Benner Peter
Published: December 2018

This paper deals with a mathematical model of the preferential crystallization of enantiomers. The dynamics is governed by two first‐order partial differential equations with controls appearing in the coefficients and in the boundary conditions. We study the problem of stabilizing the equilibrium of this system by a one‐dimensional input. For this purpose we construct a Lyapunov functional in the integral form whose density is defined through solutions of auxiliary ordinary differential equations. It is shown that the time derivative of this functional along the trajectories of the closed‐loop system is negative semidefinite. We also discuss some extensions of these results for the construction of a strict Lyapunov functional.
Model and Parameter Study of a Shape‐Adaptable Beam for Vibration Control
Authors: Nowak Alexander , Willner Kai , Hasse Alexander
Published: December 2018

Shape adaptation is an effective approach for vibration damping. In this context, a numerical model of a slender, shape‐adaptable beam is introduced. The beam is essentially an arrangement of compliant ribs which are interconnected by a hull structure. The compliant ribs are characterized by at least two desired deformations modes with a low modal stiffness, whereas the remaining modes are considerably stiffer. By actively exciting the first desired deformation mode, the cross‐sectional stiffness of the beam can be altered between a low and a high stiffness state and therefore, the vibration behavior of the beam can be influenced.

In detail, this paper presents a surrogate model of the compliant ribs which easily allows for modifying the stiffness properties of the ribs by a low number of parameters. The surrogate model is integrated in the FE‐modelled hull structure in order to simulate the 3D behavior of the entire structure. The influence of shape adaptation on the dynamic behavior of the free vibrating beam as well as for excited oscillation is examined. Especially, modal energies and their transfer between the modes due to the shape adaptation are considered. In addition, we are conducting a study on the parameters of the surrogate model in order to gain a deeper insight into the complex interrelationships of vibration reduction through shape adaptation.
Taylor approximation for PDE‐constrained optimization under uncertainty: Application to turbulent jet flow
Authors: Chen Peng , Villa Umberto , Ghattas Omar
Published: December 2018

We present a scalable method for PDE‐constrained optimization under high‐dimensional uncertainty. The method is based on a functional Taylor approximation of the cost functional with respect to (w.r.t.) the random parameter field. We consider a risk‐averse optimization formulation via a mean‐variance measure for the control objective. A quadratic Taylor approximation of the control objective gives rise to a function involving the trace of the Hessian of the objective w.r.t. the random parameter, preconditioned by the covariance operator. We apply a randomized SVD algorithm to estimate the trace, which is demonstrated to be scalable w.r.t. the parameter dimension, i.e., the number of PDE solves is independent of the parameter dimension and depends only on the decay of the eigenvalues of the covariance‐preconditioned Hessian (which is typically dimension‐independent). We solve the resulting generalized eigenproblem‐constrained optimization problem by a quasi‐Newton method. We apply our method to a RANS turbulence model with an infinite‐dimensional random field representing model inadequacy, and demonstrate scalability on discretized problems with parameter dimensions up to one million.
A new material approach towards shear cutting of fiber reinforced plastics
Authors: Poggenpohl Lukas , Wulfinghoff Stephan , Reese Stefanie
Published: December 2018

The aim of this project is to develop and validate a new material model to simulate the material behavior of carbon fiber reinforced plastics (CFRP) during shear cutting. Here, the focus lies on the initiation and evolution of damage in the cutting plane. A geometrically nonlinear elastic‐brittle material model with non local damage variables will be used.
Passive Vibration Control by Frictional Energy Dissipation in Refrigerant‐Lubricated Gas Foil Bearing Rotor Systems
Authors: Leister Tim , Seemann Wolfgang , Bou‐Saïd Benyebka
Published: December 2018

Even though the dynamic performance of rotors supported by refrigerant‐lubricated gas foil bearings (GFBs) is very sensitive to the amount of energy dissipated in the foil structure, almost none of the existing computational models really capture dry friction with typical stick–slip transitions. The presented work addresses this shortcoming by incorporating an elasto‐plastic bristle friction law into the structural model, which is coupled in an interconnected solution approach to a Reynolds equation for non‐ideal compressible gases and to a modified Jeffcott–Laval rotor model. Numerical results confirm that properly designed GFBs have the potential to benefit significantly from the foil structure acting as a passive vibration control device.