bluuebunny/crossref_metadata_2025_split huggingface dataset:
A model order reduction technique for FFT‐based microstructure simulation using a geometrically adapted reduced set of frequencies
Authors: Gierden Christian , Waimann Johanna , Svendsen Bob , Reese Stefanie 
Published: December 2021

AbstractThe FFT‐based method introduced by Moulinec and Suquet [9] serves as an alternative for the classical finite element based simulation of periodic microstructures. This simulation approach makes use of fast Fourier transforms (FFT) as well as fixed‐point iterations to solve the microscopic boundary value problem which is captured by the Lippmann‐Schwinger equation. Kochmann et al. [5] introduced a model order reduction technique using a reduced set of frequencies to decrease the computational effort of solving the Lippmann‐Schwinger equation in Fourier space. This earlier proposed method is based on a fixed sampling pattern, which determines the reduced set of frequencies. Instead of the fixed sampling pattern, we propose to use a geometrically adapted choice of frequencies, which corresponds to the representation of phases within the considered microstructure.
Analytical and numerical approach on quenching friction‐induced oscillations in MDOF‐systems by the use of high‐frequency excitation
Authors: Keller Simon , Seemann Wolfgang 
Published: December 2021

AbstractDry friction is well known to lead to undesired, self‐excited vibrations which negatively influence a process or cause discomfort. One attempt to quench these oscillations are superposed high‐frequency vibrations. A system consisting of two visco‐elastically coupled masses on a moving belt subject to high‐frequency excitation is analyzed. A multiple scales method is used to find an analytical approach of the system dynamics, which leads to the equation for the slow motion of the system, which is of interest. Linearizing about the quasi‐equilibrium and analyzing the eigenvalues, statements about the stability of the new equilibrium point can be given. These semi‐analytical results are compared to the numerical solution of the full system and the influence of certain parameters is outlined.
Minimality of Linear Switched Systems with known switching signal
Authors: Hossain Md Sumon , Trenn Stephan 
Published: December 2021

AbstractMinimal realization is discussed for linear switched systems with a given switching signal. We propose a consecutive forward and backward approach for the time‐interval of interest. The forward approach refers to extending the reachable subspace at each switching time by taking into account the nonzero reachable space from the previous mode. Afterwards, the backward approach extends the observable subspace of the current mode by taking observability information from the next mode into account. This results in an overall reduced switched system which is minimal and has the same input‐output behavior as original system. Some examples are provided to illustrate the approach.
Adaptive Exponential Finite Elements for a Phase Field Fracture Model
Authors: Olesch Darius , Kuhn Charlotte , Schlülter Alexander , Müller Ralf 
Published: December 2021

AbstractFracture phenomena can be described by a phase field model in which an independent scalar field variable in addition to the mechanical displacement is considered [3]. This field approximates crack surfaces as a continuous transition zone from a value that indicates intact material to another value that represents the crack. For an accurate approximation of cracks, narrow transition zones resulting in steep gradients of the fracture field are required. This necessitates a high mesh density in finite element simulations, which leads to an increased computational effort. In order to circumvent this problem without forfeiting accuracy, exponential shape functions were introduced in the discretization of the phase field variable, see [4]. These special shape functions allow for a better approximation of steep gradients of the phase field with less elements as compared to standard Lagrange elements. Unfortunately, the orientation of the exponential shape functions is not uniquely determined and needs to be set up in the correct way in order to improve the approximation of smooth cracks. This work solves the issue by adaptively reorientating the exponential shape functions according to the nodal values of the phase field gradient in each element. Furthermore, a local approach is pursued that uses exponential shape function only in the vicinity of the crack, whereas standard bilinear shape function are used away from the crack.
Coarse‐graining via EDP‐convergence for linear fast‐slow reaction‐diffusion systems
Authors: Stephan Artur 
Published: December 2021

AbstractIn [7] a fast‐reaction limit for a linear reaction‐diffusion system consisting of two diffusion equations coupled by a linear reaction is performed. The linear reaction‐diffusion system is understood as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh‐type functions for the reaction part. The fast‐reaction limit is done on the level of the gradient system by proving EDP‐convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow‐manifold. Moreover, the limit gradient system can be equivalently described by a coarse‐grained gradient system, which induces a scalar diffusion equation with a mixed diffusion constant for the coarse‐grained slow variable.
Phase field modeling of crack nucleation and propagation in martensitic micro–structures
Authors: Borzabadi Farahani Ehsan , Juhre Daniel 
Published: December 2021

AbstractIn this paper, a combined phase‐field (PF) approach has been considered to model fracture behavior under martensitic transformation effects. The effect of temperature as another degree of freedom has been studied, which has not been taken into account in previous studies. The concept of thermodynamic driving force, the elastic energy, interfacial energy, heat transfer and the kinetics of phase field equations are introduced to obtain the fracture domain, the martensitic evaluation, the temperature field and displacements [1]. Due to the high amount of stress at the crack tip, the martensitic transformation can start and propagate through the austenitic structure. The internal stresses between martensitic and austenitic layers deviate the crack path, leading to changes in the martensitic formation [2]. In addition, temperature plays an important role in this phenomenon in two aspects; first of all a change in temperature can produce thermal stress; and secondly, it affects the conditions for martensitic transformation. An increase in temperature requires more energy for the phase transformation [3], and changes in martensitic formation induce a new driving force for crack growth [2,4].
Prediction of the anisotropic crack resistance of heterogeneous microstructures using a crack phase‐field model
Authors: Hansen-Dörr Arne Claus , Kästner Markus 
Published: December 2021

AbstractIn this contribution, a variational crack phase‐field model for heterogeneous materials is used to study periodic microstructures. The discontinuity at material interfaces is taken into account by an additional static order parameter. A partial rank‐I relaxation ensures the pointwise fulfillment of the Hadamard jump condition and static equilibrium within the diffuse interface. Crack propagation is investigated for different orientations of hexagonal microstructures and various phenomena like toughening‐by‐weakening and an orientation‐dependent fracture toughness are observed.
Nonlocal damage modelling for finite element simulations of ductile steel sheets under multiaxial loading
Authors: Nahrmann Marvin , Matzenmiller Anton 
Published: December 2021

AbstractThe finite element simulation of forming processes or vehicle crash scenarios involves multiaxial loading conditions in general. Thereby, damage and failure in ductile steel sheets is triggered by void growth under hydrostatic tensile loading or by void elongation within a narrow band under shear dominated loading. These different damage mechanisms are considered by a stress state dependent continuum damage model. The damage initiation and failure are represented by a critical and a failure strain. Both are HOSFORD‐COULOMB type functions of the stress triaxiality and the LODE parameter and, thus, incorporate the stress state dependence of the damage mechanisms. Due to the pathological mesh sensitivity for continuum damage models, an enhancement towards nonlocal damage evolution is carried out. Thereby, two options are investigated and compared: the integral nonlocal formulation and the gradient enhanced approach. Finally, the proposed nonlocal ductile damage model is verified for a wide range of stress states by test data of various tensile and shear specimens.
Forward dynamics simulation of a human leg model with a geometrically exact beam model as prosthetic foot.
Authors: Scheiterer Eduard S. , Leyendecker Sigrid 
Published: December 2021

AbstractIn this work, we present a model for a human leg with a prosthetic foot, consisting of rigid bodies for the thigh and shank and a geometrically exact beam model for the prosthesis. The prosthesis is modelled after the Össur Vari‐Flex® carbon spring prosthetic foot. The individual bodies are connected by joints imposing constraints, mimicking the motions of human joints. A structure preserving variational integrator is used to calculate the forward dynamic simulation of the model and to analyse the energy exchange between potential, kinetic and deformation energy. Due to the variational integrator, there is no artificial energy loss introduced by the numerical integration over the simulation time [3].
Dynamic simulation of the Wilberforce pendulum using constrained spatial nonlinear beam finite elements
Authors: Harsch Jonas , Capobianco Giuseppe , Eugster Simon R. 
Published: December 2021

AbstractMore than 100 years ago, Lionel Robert Wilberforce did investigations On the Vibrations of a Loaded Spiral Spring [1]. The spring was clamped at its upper side and on the other side, perpendicular to the spring axis, a steel cylinder was attached. Four screws with adjustable nuts were symmetrically attached around the cylinder in order to change its moment of inertia (Fig. 1). In this paper the Wilberforce pendulum is modeled by a rigid body attached to a constrained spatial nonlinear Timoshenko beam, discretized with B‐spline shape functions. As shown by a numerical experiment, the presented model is capable of reproducing the characteristic pendulum motion.
Simulation of ductile crack propagation in metal matrix composites ‐ Comparison with cyclic experiments
Authors: Wingender Dennis , Brackmann Lukas , Röttger Arne , Balzani Daniel 
Published: December 2021

AbstractThe efficient operation of mechanized tunnel drilling machines is strongly determined by the wear resistance of the applied mining tools. Especially in chisels, but also partly in cutting disks, metal matrix composites are used. Their wear mechanism is dominated by surface spalling, i.e. subcritical crack propagation through the material's microstructure, mainly consisting of a ductile metal matrix and carbide inclusions. Since this process is primarily governed by the morphology of the microstructure and the mechanical behavior of the individual phases, simulations at the microscale enable the design of improved materials. In this contribution, a method for the modeling of this process is presented. The approach is based on the eigenerosion framework introduced in [1] and an algorithmic scheme for large strains is given, which extends the small strain implementation in [2]. For the phases at the microscale, the finite strain plasticity formulation [3] is applied. Examples according to [4] are shown in order to demonstrate the mesh independence of the framework for ductile crack propagation. Furthermore, simulations are carried out on the microscale by applying the Finite Cell Method [5] on metal matrix composite microstructures. Here, a specific cell arrangement is constructed which minimizes the required number of cells for a given microstructure morphology. Additionally, an experimental setup for the validation of the eigenerosion framework on the microscale is presented. By evaluating the results of these simulations, failure of the material can be investigated on a microscopic level and improvements of the material morphology regarding wear can be realized.
Multiscale modeling of calcified hydrogel networks
Authors: Aygün Serhat , Klinge Sandra 
Published: December 2021

AbstractThe model proposed simulates the effective material behavior of calcified hydrogels using the multiscale finite element method (FEM). To this end, representative volume elements (RVEs) are generated to depict the biphasic material microstructure consisting of the organic hydrogel and inorganic calcium phosphate. The choice of the hydrogel matrix influences the type of agglomeration of the inorganic phase and thus dictates the geometry of the RVE. Most commonly, the inorganic phase appears in the form of spherical inclusions or honeycomb grids where the characteristic size of a typical unit may vary. The approach proposed treats the calcified regions as Neo‐Hookean material and assumes the Ogden model for the hydrogel. The contribution closes with the numerical results on the effective material behavior and their validation with respect to experimental findings.
Simulation of the dynamic properties of open cell foams by means of a macroscopic stochastic model
Authors: Kirchhof Stephan , Ams Alfons 
Published: December 2021

AbstractOpen cell foams are widely used in engineering which includes an application in areas, where vibration excitations can act on the structures. Therefore dynamical properties as eigenfrequencies and eigenmodes are of particular interest, which show a dispersion due to the stochastic characteristic of the microstructure. To avoid time consuming measurements a simulation algorithm will be presented which enables to estimate the distribution of the eigenfrequencies. In order to do this the microstructure has to be addressed as well as different weights of several specimen, which have an influence on the computed and measured eigenfrequencies.
Plate theories: A‐priori fulfillment of the local conditions by the consistent‐approximation approach
Authors: Meyer-Coors Michael , Kienzler Reinhold , Schneider Patrick 
Published: December 2021

AbstractClassical plates theories, like Kirchhoff's plate theory [1], are based on kinematical a‐priori assumptions. Avoiding these assumptions, we derive from the three‐dimensional theory of linear elasticity by means of Taylor‐series expansions the quasi two‐dimensional problem. This problem consists of infinitely many partial‐differential equations (PDEs) written in infinitely many displacement coefficients. With the consistent approximation approach we arrive at solvable hierarchical plate theories. By using the modular structure of the displacements coefficients (modularity), we obtain from these generic‐plate theories the complete‐plate theories, whose results fulfill the strong form of the local equilibrium conditions and the Neumann boundary conditions on the upper and lower face of the plate (local conditions) a‐priori. Furthermore, we show that every variable of the complete‐plate theories can be calculated.
Curvature sensing of a soft robot based on conductive foam
Authors: Grube Malte , Seifried Robert 
Published: December 2021

AbstractSoft material robots are an emerging and fast‐growing field of research [1] with potential application in various technical fields. These applications include, but are not limited to medical applications and all sorts of human‐machine‐interaction. Due to the soft structure, conventional components and design methodologies are not applicable. For reliable control and positioning of soft robots in 3D space especially accurate knowledge about their current position and orientation is essential.In this contribution, a resistive curvature sensor for a soft robot is presented. It is based on electrically conductive foam attached to the soft robot. Deformations of the foam lead to a change in electrical resistance [2] which can be measured and used to determine the curvature of a soft robot. Since the sensor behavior is nonlinear and hysteretic, a neural network is used to determine the curvature of the soft robot from the measured foam resistances.
A Mixed Acoustic Fluid Finite Element in Boundary Representation for Fluid‐Structure Interaction
Authors: Sauren Bjorn , Klarmann Simon , Klinkel Sven 
Published: December 2021

AbstractThis contribution focuses on a mixed finite element formulation for an acoustic fluid in boundary representation to model fluid‐structure interaction problems. In fact, acoustic fluids are characterized by their lack of dynamic viscosity and undergo displacements through a pure pressure wave propagation. Since many fluids, for instance water, show nearly‐incompressible behavior, volumetric locking occurs in the classical finite element formulation. This drawback is herein evaded by a two‐field, or mixed, finite element formulation. To facilitate the contact condition at the fluid‐structure interface, the acoustic fluid is expressed by structural field variables, which are nodal displacements and internal pressures. Both the displacements and internal pressures are parameterized by a Scaled‐Boundary (SB) approach, in which an interpolation in the scaling direction is employed. From this parametrization, the element mass and stiffness matrices of the fluid can be formulated. Due to the special parametrization of the element boundary, pressure continuity is required between scaled sections in the element interior, although pressure continuity may be interrupted between neighboring Scaled‐Boundary elements. Since the lack of shear viscosity leads to unwanted zero‐energy modes concerned with the fluid's vorticity, this vorticity is penalized on a sectional level. As a result, these modes do not show up in the frequency spectrum of the dynamic eigenvalue problem any longer. The natural frequencies and mode shapes in this spectrum deliver accurate results, even for very coarse meshes.
Configurational Forces in Bond Order Potentials
Authors: Birang O. S. Elmira , Smith Ana-Suncana , Steinmann Paul 
Published: December 2021

AbstractIn this contribution, a configurational mechanics framework is elaborated to assess the applicability of atomistic configurational forces in fracture of crystalline lattices. To this end, an analytical interatomic potential is reformulated in terms of the material positions occupied by the atoms participating in two‐ and three‐body interactions. It is demonstrated that such a potential satisfies the requirements of invariances i.e., translational, rotational and parity. The focus of this work is developing the configurational setting for the bond order Tersoff potential. Two‐dimensional pre‐cracked mono‐layer graphene modelled with the Tersoff potential is chosen to study the configurational force approach in determining energy release during crack propagation into the lattice.
Frequency analysis of transversal vibrations of belt drives with time‐varying belt lengths
Authors: Schnürer Dominik , Holl Helmut J. 
Published: December 2021

AbstractThe dynamic positioning accuracy and the smoothness are key aspects of linear belt drives where vibrations have a negative impact. A FE‐Model, based on a one‐dimensional analytical model of the belt, is derived to study the respective effects for different parameters. The model considers the dominant transverse deflection and a quasi‐static assumption for the longitudinal deformation. The possibility to consider various time‐varying belt lengths, the belt mass, stiffness and tension force is an essential part of the modeling. The non‐linear cable effect is demonstrated by comparison with the linearized solution. Vibrations for the cases of constant and variable belt length are investigated and compared to common in literature used approximation formulas for the resonance frequencies of such systems. The influence on positioning deviations and the use of vibration reduction techniques considering the different belt sections of the linear drive can be derived from the computed results and are topics for future research.
Application of a continuum‐mechanical tumour model to brain tissue
Authors: Suditsch M. , Lambers L. , Ricken T. , Wagner A. 
Published: December 2021

AbstractBrain tumours are among the most serious diseases of our time. A continuum‐mechanical model is proposed to represent the basic processes of growth and regression. The physical multi‐constituent approach is derived in the framework of the Theory of Porous Media (TPM). This modelling approach can be expressed mathematically via strongly coupled partial differential equations (PDEs), that are solved using the well‐known Finite Element Method with the software toolkit FEniCS. A realistic initial‐boundary‐value problem is used to demonstrate the workflow with the used software and the capabilities of the model.
Simulation of fatigue crack growth in residual‐stress‐afflicted specimen with a phase‐field model
Authors: Seiler Martha , Keller Sören , Kashaev Nikolai , Klusemann Benjamin , Kästner Markus 
Published: December 2021

AbstractLaser shock peening (LSP) is a promising technique to systematically introduce local compressive residual stresses in metal sheets, inhibiting fatigue cracks in these areas. We model fatigue crack growth in these specimen with the help of a phase‐field model for fatigue fracture [1]. First, we parametrise the model using untreated aluminium specimens. In a second step, we use the determined parameters to simulate residual‐stress‐afflicted specimens, qualitatively reproducing the crack inhibition due to LSP.
Phase field method for quasi‐static brittle fracture: an adaptive algorithm based on the dual variable
Authors: Bertrand Fleurianne 
Published: December 2021

AbstractAn adaptive phase field method for quasi‐static brittle fracture is developed. The adaptive refinement of the meshes is based on the error between two stresses: the discontinuous post‐processed stresses computed with the displacement approximation and a H(div) conforming dual approximation of the stresses. The algorithm is validated by solving a benchmark problem considering a plate with an edge crack subjected to tension load.
Towards the application of the One‐Dimensional Turbulence model for the evaluation of collection efficiencies in wire‐tube electrostatic precipitators
Authors: Medina Méndez Juan A. , Schmidt Heiko 
Published: December 2021

AbstractThe One‐Dimensional Turbulence (ODT) model framework for the simulation of particle‐laden wire‐tube electrostatic precipitators is detailed in this work by specifying initial conditions, governing equations, and the mechanism for two‐way coupling between the electrostatic fields and the hydrodynamic flow. Unlike in a previous investigation [1], a two‐way coupling is required due to the low electrical mobility of aerosol particles, making flow motion responsible for the appearance of electrical convective currents. The ultimate goal of this framework is to develop a method which is able to investigate the precipitation phenomenon in wire‐tube precipitators, e.g., the collection efficiency, while relying on highly resolved physics.