bluuebunny/crossref_metadata_2025 huggingface dataset:
A Pin‐on‐Disk Experimental Set‐up for Vibrational Smoothing of Dry Friction
Authors: Kapelke Simon , Seemann Wolfgang
Published: October 2016

High‐frequency vibrations have been shown to smooth the effective characteristics of dry friction and may be used in order to quench undesired phenomena such as friction induced vibrations. Recent contributions have discussed the influence of contact compliance on vibrational smoothing. Within this contribution, an experimental set‐up is presented, which has been developed in order to validate the calculated results. After a brief description, some general properties of the system are investigated, including stationary and oscillatory behaviour. Without vibrational excitation, friction induced vibrations occur at low sliding velocities. The corresponding motion of the system is analysed and compared to the results of FE‐based simulations. Finally, a first attempt is presented reducing the average friction force by imposing appropriate vibrations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Synchronization effects in rotors partially filled with fluid‐influence on propulsion
Authors: Keisenberg Tobias , Ostermeyer Georg‐Peter
Published: October 2016

In fluid‐filled Rotors occur self‐excited vibrations induced by surface waves of the fluid. A characteristic property is the instability over an interval of angular velocity above the natural frequency of the system. One explanation is the occurrence of synchronization effects between fluid waves and the critical rotor speed.

The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady‐state conditions. For non‐steady‐state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable for observer‐based real‐time control.

This paper analyses a model based on a laval rotor and shows synchronization effects between fluid waves and rotor model and its influence on the rotor propulsion. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Vibrations of Rotors Supported on Nonlinear Bearings
Authors: Mair Mathias , Haas Stefan , Ellermann Katrin
Published: October 2016

Rotors in electrical machines are supported by various types of bearings. In general, the rotor bearings have nonlinear stiffness properties and they influence the rotor vibrations significantly. In this work, this influence of these nonlinearities is investigated. A simplified finite element model using Timoshenko beam elements is set up for the heterogeneous structure of the rotor. A transversally isotropic material model is adopted for the rotor core stack. Imposing the nonlinear bearing stiffnesses on the model, the Newton‐Raphson procedure is used to carry out a run up simulation. The spectral content of these results shows nonlinear effects due to the bearings. The rotor vibrations are further investigated in detail for various constant speeds. These results show non‐harmonic vibrations of the rotor in a section of the investigated speed range. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the refined modeling of the force distribution in a bistable magnetoelastic energy harvesting system due to a magnetic field
Authors: Noll Max‐Uwe , Lentz Lukas
Published: October 2016

Abstract: The problem of a bistable magnetoelastic beam under base excitation was discussed in [1] under the aspect of chaotic behaviour in mechanical systems. Three decades later the system was used in [2] to design an energy harvesting system which performs well under harmonic excitation for a broad range of excitation frequencies due to its bistability. The initial modeling was tailored to obtain a model with one degree of freedom based on the assumption that the magnetic force acts on the beam tip only. A more appropriate model can be found when considering a distributed force along the beam.

The authors present the force distribution on a ferromagnetic beam due to the magnetic field of two permanent magnets. A semi‐analytic method is used to compute the magnetic field. The force distribution can in future be used to derive a refined nonlinear dynamical model for the ferromagnetic elastic beam. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hopf‐Takens‐Bogdanov interaction for a fluid‐conveying tube
Authors: Steindl Alois
Published: October 2016

We investigate the dynamics after loss of stability of the downhanging configuration of a fluid conveying tube with a small end mass and an elastic support.

By varying the fluid flow rate and the stiffness and location of the elastic support, different degenerate bifurcation scenarios can be observed. In this article we investigate the bifurcating solution branches of the codimension 3 interaction between a Hopf bifurcation and a Bogdanov‐Takens bifurcation.

A complete discussion of the primary and secondary solution branches was already given by W. F. Langford and K. Zhan. After reducing the system to the three‐dimensional Normal Form equations we apply a numerical continuation procedure to locate the expected higher order bifurcation branches and detect more complicated dynamics, like Shilnikov orbits. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental and theoretical investigation of creep groan of brakes through minimal models
Authors: Zhao Xingwei , Gräbner Nils , von Wagner Utz
Published: October 2016

Creep groan of brake systems is a low frequency vibration phenomenon occurring at low speeds which can make passengers feel uncomfortable. This phenomenon is caused by the stick‐slip‐effect resulting in limit cycle oscillations with frequencies lower than 200 Hz. For the experimental investigation of this problem, an idealized brake test rig is designed concentrating on the investigation of the frictional contact by realizing low damping and small disturbances in the system. Different sensors are utilized in the test rig. Limit cycles and bifurcation effects can be observed in the experimental results. With respect to modeling, a one degree‐of‐freedom (DOF) model using Coulomb's friction law and a two DOF model using the bristle friction law are considered. In a comparative study of experimental and simulation results, the parameters of both friction laws can be identified from the dynamic experimental results, such as the static and dynamic friction coefficients, contact stiffness and Stribeck velocity. Experimental and theoretical results show a very good concordance. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled finite element approach for the modelling of composites with fibres possessing fibre‐bending stiffness
Authors: Asmanoglo Tobias , Menzel Andreas
Published: October 2016

The algorithmic implementation of a constitutive model for fibre‐reinforced materials with fibre‐bending stiffness, in addition to the classical directional contributions of the fibres, is presented. Based on theoretical investigations presented in [1], the numerical solution of the underlying non‐linear system of coupled partial differential equations by means of a mixed‐type multi‐field finite element approach is discussed. To this end, additional field variables are introduced to approximate higher‐order gradients which enter the proposed energy function of the extended continuum and, accordingly, introduce a size effect into the model. Concluding, representative boundary value problems are solved to analyse the basic properties of the model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DEM‐FEM coupled numerical investigation of granular materials to increase crashworthiness of double‐hull vessels
Authors: Chaudry Mohsin Ali , Woitzik Christian , Weißenfels Christian , Düster Alexander , Wriggers Peter
Published: October 2016

In this contribution, a novel design strategy is investigated for improving the crashworthiness of double‐hull vessels, which involves usage of granular materials. For numerical simulation, a framework based on coupling of the Discrete Element and the Finite Element Method is used to study load bearing capacity of granular materials during uniaxial compression. In addition, the effect of Young's modulus of particles is also investigated with respect to the load transferability. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling of hydrodynamic strain amplification in filled elastomers
Authors: Darabi Ehsan , Itskov Mikhail , Klüppel Manfred
Published: October 2016

Polymer chains in filled elastomers are subject to a strain bigger than the overall (macro‐strain) applied to the specimen, which is described by a strain amplification factor. In the current paper, a micromechanical model for hydrodynamic strain amplification is presented. To this end, we develop the concept of the multiple filler fractions within the so‐called Dynamic Flocculation Model (DFM) framework. Accordingly, with increasing strain, a single unbroken virgin cluster gradually splits into smaller clusters. Thus, fractions of smaller filler clusters increase with the increasing strain, which in turn influences the filler‐induced hysteresis. The filler induced hysteresis is then described by the cyclic breakdown of the residual fragile filler clusters and re‐aggregation of the already broken filler‐filler bonds. The model includes a few number of physically motivated material constants describing the average filler cluster dimensions, filler‐filler and filler‐matrix interaction properties. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A thermodynamic framework for coupled multiphase field and diffusion models for lower bainite transformation
Authors: Düsing Martin , Mahnken Rolf
Published: October 2016

The lower bainite transformation is characterized by a displacive transformation from austenite to bainitic ferrite and a subsequent separation of carbon within the new supersaturated phase. At accumulations of carbon carbides precipitate. To model this complex process a framework considering phase changes and carbon diffusion is required. In this work we present a thermodynamic framework based on the theory of microforce balances considering multiphase Ginzburg‐Landau equations coupled with Cahn‐Hilliard diffusion. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crysal Plasticity Finite Element Simulations based on Continuum Dislocation Dynamics
Authors: Ebrahimi Alireza , Hochrainer Thomas
Published: October 2016

Plastic deformation of crystalline materials is the result of the motion and interaction of dislocations. Continuum dislocation dynamics (CDD) defines flux‐type evolution equations of dislocation variables which can capture the kinematics of moving curved dislocations. Coupled with Orowan's law, which connects the plastic shear rate to the dislocation flux, CDD defines a dislocation density based material law for crystal plasticity.

In the current work we provide simulations of a micro‐bending experiment of a single crystal and compare the results qualitatively to those from discrete dislocation simulations from the literature. We show that CDD reproduces salient features from discrete dislocation simulations regarding the stress distribution, the dislocation density and the accumulated plastic shear, which would be hard to obtain from more traditional crystal plasticity constitutive laws. © 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An alternative perspective on the concept of stress in classical continuum mechanics
Authors: Eugster Simon R. , Glocker Christoph
Published: October 2016

Within a variational formulation of continuum mechanics, as proposed for instance by Germain [1], the internal virtual work contribution of a continuum is postulated as a smooth density integrated over the deformed configuration of the body. In this smooth density the stress field appears as dual quantity to the gradient of the virtual displacement field. Since the mathematical definition of the volume integral naturally provides a macro‐micro relation between infinitesimal volume elements and the continuous body, we propose in this paper an alternative definition of stress on the micro level of the infinitesimal volume elements. In particular, the stress is defined as the internal forces of the body that model the mutual force interaction between neighboring volume elements. The existence of the stress tensor on the macro level is then obtained from the summation of all virtual work contributions within the body, followed by a limit process in which the volume elements are sent to zero. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A computational two scaled model for the simulation of micro‐heterogeneous low‐alloyed TRIP steels
Authors: Gandhi Ashutosh , Prüger Stefan , Balzani Daniel
Published: October 2016

In transformation induced plasticity (TRIP) steel a diffusionless austenitic‐martensitic phase transformation induced by plastic deformation can be observed, resulting in excellent macroscopic properties. In particular low‐alloyed TRIP steels, which can be obtained at lower production costs than high‐alloyed TRIP steel, combine this mechanism with a heterogeneous arrangement of different phases at the microscale, namely ferrite, bainite, and retained austenite. The macroscopic behavior is governed by a complex interaction of the phases at the micro‐level and the inelastic phase transformation from retained austenite to martensite. A reliable model for low‐alloyed TRIP steel should therefore account for these microstructural processes to achieve an accurate macroscopic prediction. To enable this, we focus on a multiscale method often referred to as FE2 approach, see [6]. In order to obtain a reasonable representative volume element, a three‐dimensional statistically similar representative volume element (SSRVE) [1] can be used. Thereby, also computational costs associated with FE2 calculations can be significantly reduced at a comparable prediction quality. The material model used here to capture the above mentioned microstructural phase transformation is based on [3] which was proposed for high alloyed TRIP steels, see also e.g. [8]. Computations based on the proposed two‐scale approach are presented here for a three dimensional boundary value problem to show the evolution of phase transformation at the microscale and its effects on the macroscopic properties. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A consistent implementation for inelastic materials in an ALE formulation for steady state rolling contact
Authors: Garcia Mario A. , Kaliske Michael
Published: October 2016

The numerical analysis of rolling contact for rubber materials is a challenging task, especially due to the many nonlinearities inherent to the material, large deformations, friction, and energy dissipation, among others. Industrial applications can be found in ball bearings, rollers, and most commonly in tires of vehicles, applications where reliable numerical simulations lead to the improvement of durability, performance and safety. While a transient analysis stands as a practical and powerful tool for the simulation of rotating bodies, the large amount of computational resources required represents its biggest disadvantage. An alternative frequently used lays in a steady state simulation by means of an Arbitrary Lagrangian Eulerian (ALE) formulation, where the rotational velocity and axial loads are assumed to remain constant. Within this framework, the reference configuration is neither attached to the material particles nor fixed in space and special attention should be paid to the history variables of inelastic materials. In this work, a viscoelastic material model is implemented in an in‐house finite element code, based on a generalized Maxwell model. The implementation takes into consideration the contribution of all elements connected in circumferential direction and a consistent linearization is made for each of them, leading to an assembled stiffness matrix with more non‐zero values than a standard one. This approach is combined with smeared reinforcement embedded in base elements. The reinforcing layers are described by a hyperelastic material model, providing additional advantages for the modeling and simulation of reinforced rollers and tires. Numerical results for different examples show the capabilities of this implementation and the efficiency of the numerical algorithms is discussed. Important remarks and an outlook for further research concludes this presentation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The effective heat conduction of short fibre reinforced materials considering the fibre distribution
Authors: Goldberg Niels , Ihlemann Jörn
Published: October 2016

This contribution focuses on the effective heat conductivity of short fibre reinforced materials. For this purpose, a representative volume element (RVE), which is able to represent all possible fibre orientation distributions, is introduced and modelled in ABAQUS. Subsequently, the effective heat conductivity of the RVE is derived, employing a numerical homogenisation scheme, and a phenomenological material model is fitted to those results. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental and numerical investigation of metal foams undergoing large deformations
Authors: Heinze Stephan , Jung Anne , Diebels Stefan , Düster Alexander
Published: October 2016

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT‐image of the foam. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromorphic Homogenisation of a Porous Medium: Application to Size Effects and Quasi‐Brittle Damage
Authors: Hütter Geralf , Skrypnyk Rostyslav
Published: October 2016

The classical theory of continuum mechanics requires that distances over which gradients occur are much larger than the length scales of the microstructure. This requirement is violated if deformation localizes due to material softening which is why the predictions of classical damage models feature certain unrealistic aspects. In the present contribution, a micromorphic model for quasi‐brittle damage, derived through homogenisation, is employed in FEM simulations to overcome this problem. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of thick adhesive layers at finite strains utilizing an associated flow rule in a thermodynamically consistent framework
Authors: Kieser Florian , Klinkel Sven
Published: October 2016

The application of elastoplastic material models is commonly used for the modelling of adhesive layers with high strength adhesives as realized with polyurethane or epoxy resin. To fulfill thermodynamic consistency often restrictions on the choice of material parameters are requested. One of them is the introduction of a non‐associated flow rule, which always ensures positive dissipation. Nevertheless, this assumption is a non‐essential criterion, which will be addressed in this work. Continuing along this argumentation, the constitutive relations for the material is modified based on an associated flow rule. The applied model for the simulation of the adhesives is based on a small strain theory. A yield surface including two stress invariants, the hydrostatic pressure as well as the deviator stress state, set the elastic limit of the material response. Linear as well as exponential hardening is incorporated and material softening that arises subsequently is also included by substituting effective invariants in the yield function. This material model as proposed from literature was extended to finite strain application with the concept of generalized stress‐strain‐measure, which was realized in a previous work. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of microstructural pattern formation in crystal plasticity
Authors: Klusemann Benjamin
Published: October 2016

The mechanical behavior of most materials is dictated by a present or emergent underlying microstructure which is a direct result of different, even competing physical mechanisms occurring at lower length scales. In this work, energetic microstructure interaction via different non‐convex contributions to the free energy in metals is modeled. For this purpose rate dependent gradient extended crystal plasticity models at the glide‐system level are formulated. The non‐convex energy serves as the driving force for the emergent microstructure. The competition between the kinetics and the relaxation of the free energy is an essential feature of the model. Non‐convexity naturally arises in finite‐deformation single‐slip crystal plasticity and the results of the gradient model for this case are compared with an effective laminate model based on energy relaxation. Similarities as well as essential differences are observed and explained. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Null‐Lagrangians and the indeterminate couple stress model
Authors: Neff Patrizio , Ghiba Ionel‐Dumitrel , Madeo Angela , Münch Ingo
Published: October 2016

The aims of this note is to present a new model based on a new representation of the curvature energy in the indeterminate couple stress model and to discuss some related choices from the literature. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling the quasi‐static mechanical behavior of the extensible worm‐like chain in the finite‐element framework
Authors: Schulz Matthias , Böl Markus
Published: October 2016

A new modeling approach for the force‐extension behavior of polymers and the solution scheme within the finite‐element framework are presented. More specifically, the first variation of the energy function of an initially curved and extensible worm‐like chain [1] and a geometrically exact beam‐element formulation [2] were used to validate the model performing an optimization procedure [3]. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental and Numerical Study of Polypropylene/Polyethylene Thin Foil in Biaxial Tension
Authors: Sguazzo Carmen , Betz Sebastian , Hartmann Stefan
Published: October 2016

The material under consideration is a thermoplastic copolymer blend of polypropylene and polyethylene (PP/PE), constituting the core layer of a steel/polymer/steel composite material. A biaxial loading machine was developed for studying the behavior of the copolymer subjected to in‐plane complex stress states. A study on the shape of the specimen by means of numerical finite element simulations and preliminary experimental tests are carried out, in order to obtain a maximization of the strain distribution in the middle region of the cruciform specimen. Afterwards, the sensitivity of the mechanical response under both equibiaxial and non‐equibiaxial conditions is addressed. All the experiments are monitored by means of a digital image correlation (DIC) system, providing full‐field measurements of the displacements, and, consequently, of the strain distribution. The presented experimental results will be used for validating the material model developed for the PP/PE layer material. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A mesoscale approach for dislocation density motion using a Runge‐Kutta discontinuous Galerkin method
Authors: Schulz Katrin , Wagner Lydia , Wieners Christian
Published: October 2016

In this note, the issue of numerical diffusion in the context of a dislocation based continuum formulation is addressed. Using a geometrical description of dislocation lines and their averages based on a higher order configuration space, a kinematic continuum model is presented for the evolution of curved dislocation lines. In order to include the physical interactions occuring between dislocation lines, an accurate numerical description of the dislocations represented by different quantities of dislocation density has to be ensured. By applying a finite volume scheme as well as a discontinuous Galerkin scheme to a simple benchmark problem, we compare the two numerical methods and discuss the results in the context of dislocation based plasticity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental and numerical investigation of granular materials for an increase of the collision safety of double‐hull vessels
Authors: Woitzik Christian , Chaudry Moshin Ali , Wriggers Peter , Düster Alexander
Published: October 2016

In the present contribution lightweight granulate like expanded glass will be considered as crash absorbing material in ship constructions. The granules were originally not intended for this application purpose, therefore the material behaviour for this load case has to be determined. To this end, the granulate is compressed in an aluminium cylinder to less than half of its initial height. Based on this experiment, the expanded glass is modelled as Mohr‐Coulomb material within a nonlinear finite element simulation and the parameters of the constitutive equations are identified from the experimental data. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Viscoelastic‐viscoplastic‐damage modeling of thermoplastics under long‐term cyclic loading
Authors: Zerbe Patrick , Schneider Benjamin , Kaliske Michael
Published: October 2016

Thermoplastics tend to creep under mechanical loads and recover deformation during unloading. A viscoelastic‐viscoplastic‐damage model is presented to accommodate the behavior of a thermoplastic under cyclic loading‐unloading. Finite element simulations may be computationally expensive in case of many loading cycles. A cycle jump method is proposed to mitigate parts of the cost. It can efficiently approximate large parts of the cyclic calculations by extrapolating internal variables over several cycles at once. Hence, only a fraction of the original computational effort remains. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computational bridge aeroelasticity using turbulence models
Authors: Alfarra Anas , Dinkler Dieter
Published: October 2016

Long‐span bridges may collapse due to the interaction of turbulent wind flow and structural motion. The investigation of the fluid‐structure interaction requires appropriate models for the structure, the wind flow and the coupling between them. Modeling and simulation of the wind flow is still a challenging aspect. The aim of this paper is to show the application of Reynolds Averaged Navier‐Stokes (RANS) equations with a turbulence model in the context of bridge aeroelasticity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fluid Structure Interaction of Blood Vessels in Circle of Willis
Authors: Alimi Aria , Wünsch Olaf
Published: October 2016

This work involves studying the role of the Brain Blood Barriers (BBB) on damping the stress applied on brain tissue through blood pressure that is the main cause of brain aneurysm. The numerical simulations are focused on the geometry of the Anterior Communicating Artery (ACoA) because there is a 30 % higher probability for a brain aneurysm in this location. A linear elastic model is used to model the structure part including BBB and brain tissue. Regarding the fluid properties, blood is assumed to behave as a Newtonian fluid. The stress and deformation of the brain tissue is analyzed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A polyconvex strain‐energy split for a high‐order phase‐field approach to fracture
Authors: Bilgen Carola , Hesch Christian , Weinberg Kerstin
Published: October 2016

This contribution focuses on a novel phase‐field model for a high‐order phase‐field approach to brittle fracture in the range finite deformation. In particular, two different challenges are tackled in this study: First, we want to establish a polyconvex free energy density to ensure the existence of a minimizer for the coupled problem, second, we have to deal with a fourth‐order Cahn‐Hilliard type equation for the approximation of the phase‐field.

Phase‐field methods employ a variational framework for brittle fracture and have proven to predict complex fracture patterns in two and three dimensional examples. Basis of the model are the conjugate stresses of the three strain measures deformation gradient (line map), its cofactor (area map) and its determinant (volume map). The introduction of the tensor cross product simplifies the presentation of the first Piola‐Kirchhoff stress tensor and its derivatives in elegant manner.

The proposed Cahn‐Hilliard type equation requires global
${\cal C}^1$
‐continuity. Therefore, we apply an isogeometric framework using NURBS basis functions. Moreover, a general hierarchical refinement scheme based on subdivision projection is used here for one, two and three dimensional simulations. This technique allows to enhance the approximation space using finer splines on each level but preserves the partition of unity as well as the continuity properties of the original discretization. We finally demonstrate the accuracy and the robustness with a series of benchmark problems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of Extrinsic and Autonomous Self‐Healing phenomena within the Framework of the Theory of Porous Media
Authors: Bluhm Joachim , Specht Steffen , Schröder Jörg
Published: October 2016

In this work a multiphase model is presented to describe the damage and healing behavior of a self‐healing microstructure. In this academic example a single microcapsule is enclosed in a polymeric matrix. Attention is payed to the outflow of the liquid healing agents from the capsule into the damaged area and the subsequent phase transition from liquid to solid. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Towards the Embedding of Relaxation‐based Magnetostriction Models into a Micromagnetically‐Motivated Finite Element Framework
Authors: Buckmann Karsten , Kiefer Björn , Bartel Thorsten , Menzel Andreas
Published: October 2016

In this contribution we present a variational framework which is suitable for the finite element implementation of energy‐relaxation based magnetostriction models. Our recent work [1] has shown that energy‐relaxation based models are able to capture all key response characteristics of multi‐ferroic magnetic shape memory alloys (MSMA). In order to simulate the response behavior of arbitrarily shaped samples we are switching to a micromagnetically inspired finite element framework [3], where the magnetization inside the magnetic material and the nonlocal demagnetization field are spatially resolved. First results compare the magnetization responses for FE‐simulations and calculations using the demagnetization tensor concept. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling Grain Coarsening in the Framework of Rational Extended Thermodynamics
Authors: Kertsch Lukas , Helm Dirk
Published: October 2016

Grain growth and shrinkage at elevated temperatures is a significant phenomenon during the processing of metals. Often, grain coarsening is described without thermodynamic considerations. But since the grain boundary mobility is thermally activated and energy stored in the grain boundaries is released during their motion, a thermodynamic framework is required to capture the various effects of the process. For this purpose, the procedure of Rational Extended Thermodynamics is applied to derive a thermodynamically consistent model for grain coarsening due to the growth and shrinkage of individual grains. Despite the different approach used, a grain growth model is obtained which is similar to existing ones and can be regarded as a thermodynamic extension of that by Hillert (1965) to more general systems. The model reproduces grain growth experiments in pure copper very accurately and predicts the associated energy release. The present approach combining a microstructure description and continuum mechanics can be further used to develop thermomechanical material models considering the microstructure. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Gradient based enhanced finite element formulation for diffuse phase interfaces
Authors: Krauss Matthias , Münch Ingo
Published: October 2016

Interfaces between adjacent phases, so‐called domain walls, appear as non‐linear gradients of order parameters in diffuse phase field models. Usually, the interface width is much smaller than the dimension of the simulated region. Since the position of domain walls is not known a priori the maximum size of finite elements needs to be adapted to the length scale of interfaces within the entire region. We suggested a selective finite element method to improve the numerical solution of diffuse phase field models [1, 2]. It enhances the finite element interpolation space using supplementary local degrees of freedom. However, corresponding additional nodes are strictly located in the interior of elements, thus, C0‐continuity at element border is guaranteed. Since C0‐continuity limits the performance of this method we propose in this paper a relaxation of C0‐requirements perpendicular to the gradient of the order parameter. Therefore, the direction of interfaces is analyzed as additional information for further adaptive improvement of the interpolation space. A dual phase field model is used to validate the proposed method. The analytical solution of a stationary domain wall allows error analysis of regular and distorted finite element meshes. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A three‐dimensional model of hydraulic fracturing
Authors: Luo Chenyi , Ehlers Wolfgang
Published: October 2016

Hydraulic fracturing, also known as “fracking”, is a common technology in the oil and gas industry. In practice, adequate fissures and cracks are generated in the stratum by injecting the fracking fluid consisting of multiple chemicals. As a result, more oil and gas are released and later extracted from the outflow. To describe the fracking process, the interaction between the soil and the fracking fluid is an important task. Another challenge comes from the description of the crack propagation, especially in the three‐dimensional case. The proposed model is based on the Theory of Porous Media (TPM), which offers a modern approach to model the biphasic, namely solid‐fluid, material. In order to simulate the crack propagation, an order parameter is included in the constitutive equations. The evolution of the order parameter is related to the stored energy of the solid. With an increasing order parameter, the stiffness of the solid and the interaction between the solid and fluid are decreasing. Hence, the material is transformed from an intact solid skeleton with a pore fluid to a broken one with a bulk fluid. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An anisotropic phase‐field model for transversely isotropic barium titanate with bounded moduli
Authors: Nadgir Omkar , Keip Marc‐André , Miehe Christian
Published: October 2016

This contribution presents a phase‐field model for transversely isotropic barium titanate, which allows for the adjustment of the full set of anisotropic material parameters. It is a direct extension of the work by Schrade et al. [1] who proposed a phase‐field model for ferroelectrics in the framework of invariant theory. In the present contribution, the loss of positive definiteness is avoided by formulating energetic terms that provide upper and lower bounds for all material moduli involved. We show the characteristics of the formulation by a set of numerical examples in two and three dimensions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A thermodynamical consistent model for modeling of ionic electroactive polymers (EAPs) within the framework of the Theory of Porous Media
Authors: Serdas Serdar , Bluhm Joachim , Schröder Jörg
Published: October 2016

Ionic electroactive polymers are widely used in many engineering fields. These kind of materials can be stimulated to change their shape and size, see [1]. Since, the material under consideration has a complex multiphasic microstructure, such multiphasic materials are best described by a continuum mechanical approach. Thus, the presented model is based on the Theory of Porous Media (TPM), cf. [2]. In this contribution, we consider the Ionic Polymer Metal Composites (IPMCs). Stimulating by an electrical voltage, a structural deformation will be caused. Responsible for this deformation are the mobile ions. The focus of the presented model is to capture this material behavior, e.g. the distribution of the mobile cations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulation of fluid‐structure interaction problems by a coupled SPH‐FEM approach
Authors: Stasch Jessica , Avci Bircan , Wriggers Peter
Published: October 2016

In scientific computing there is a great interest in numerical simulation of fluid‐structure interaction (FSI) problems. Within this work a numerical approach to simulate fluid‐structure interactions between elastic structures and weakly incompressible fluids is developed. For the fluid part and the solid part the Smoothed Particle Hydrodynamics method (SPH) and the Finite Element Method (FEM) are used, respectively. To transfer the resulting reaction forces from the fluid particles onto the structure's surface two methods are implemented, investigated and compared. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling thermoplastic material behaviour of dual‐phase steels on a microscopic length scale ‐ numerical treatment
Authors: Zeller Sebastian , Löhnert Stefan , Wriggers Peter
Published: October 2016

On a microscopic length scale dual‐phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work it is assumed that the martensitic phase behaves purely thermoelastic while for the ferritic phase a thermoplastic material model was developed based on the assumption that the driving mechanism for persistent deformation is the movement of dislocations on preferred planes in preferred directions. The necessary shear stress to move dislocations at a certain temperature and deformation rate is assumed to possess contributions from the atomic lattice, alloying atoms and the dislocation structure. To consider the influence of the dislocation structure, dislocation densities are introduced as state variables for which temperature and deformation rate dependent evolution equations are formulated. Since for general loading histories the model equations cannot be integrated analytically, a time discretized form of the model equations with an appropriate solution algorithm is presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Determination of effective properties for CFRP curing coupled to viscoleasticity based on a three‐scale framework
Authors: Dammann Christian , Mahnken Rolf
Published: October 2016

Our work presents a three‐scale model for temperature‐dependent visco‐elastic effects accompanied by curing, which are important phenomena in a resin transfer molding (RTM) process. The effective bulk quantities in dependence on the degree of cure are obtained by homogenization for a representative unit cell (micro‐RVE) on the heterogeneous microscale. To this end, an analytic solution is derived by extension of the composite spheres model [1]. Voigt and Reuss bounds resulting from the assumption of a homogeneous matrix proposed in [2] are compared to the effective quantities. During curing, the periodic mesostructure defined by a visco‐elastic polymeric matrix and linear‐thermo‐elastic fibres is taken into account as a representative unit cell (meso‐RVE) subjected to thermo‐mechanical loading on the mesoscale. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of Surface Wetting by Droplets Using a Phase Field Model
Authors: Diewald Felix , Kuhn Charlotte , Blauwhoff Ricardo , Heier Michaela , Becker Stefan , Werth Stephan , Horsch Martin , Hasse Hans , Müller Ralf
Published: October 2016

In the proposed phase field model a continuous order parameter indicates the phase distribution (liquid/gas). An energy density functional which is dependent on the surface tensions and defined by three contributions yields the total energy of the system. An equilibrium state is then computed by minimizing this energy of the system using an evolution equation. Details of the algorithmic implementation are discussed by illustrative examples. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effective plastic properties of laminates
Authors: Glüge Rainer
Published: October 2016

In this contribution, we make use of the fact homogenization of elastic properties of laminates [1] can be extended relatively easy to the plastic case [2] to derive exact expressions for the effective yield limit and the ultimate loading in monotonic tension test. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of failure in rough interfaces
Authors: Hirsch Franz , Kästner Markus
Published: October 2016

In this contribution a multiscale description of the inelastic behavior of bi‐material interfaces is considered. We study different local properties , e.g. the surface roughness, and their effects on the overall interface characteristics. Since there is a large separation of length scales between the microstructure and the macroscopic joint, we employ a numerical homogenization approach to extract effective interface properties. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model reduction and submodelling using neural networks
Authors: Koeppe Arnd , Bamer Franz , Markert Bernd
Published: October 2016

An (artificial) neural network to simulate the structural behaviour of a cluster of finite elements is proposed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Solution of Contact Problems using Level Set Methods on Voxel Discretizations
Authors: Leichner Alexander , Andrä Heiko , Simeon Bernd
Published: October 2016

Fast solvers performing on a regular grid are often used for problems in elasticity, in order to avoid expensive mesh generations. However, if overlaps between solid materials occur without any interactions, these might deteriorate the results, especially for the stresses. Therefore, we want to present an approach for developing numerical methods for contact problems on a regular mesh with the help of signed distance data and multi‐material voxels. In this contribution we will focus on problems in linear elastostatics with contact between several different bodies. Finally, we present the results from a numerical test for the two dimensional Hertz problem, solved on a triangular regular mesh. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A micromechanics model for FRC composites
Authors: Timothy Jithender J. , Zhan Yijian , Meschke Günther
Published: October 2016

A multiscale model for FRC composite structures taking into consideration the complex interactions at the scales of the fiber and microcracks is proposed. At the scale of the single fiber, a semi‐analytical model characterizes the microslip behavior at the interface between the matrix and the fiber in terms of the overall composite stresses. The influence of fiber bundles on microcrack bridging and arrest is taken into account within the framework of linear elastic fracture mechanics. Upscaling to the macroscopic level using continuum micromechanics shows that the macroscopic deformation of the FRC composite is governed by a ’TERZAGHI’ like effective stress. For the finite element analyses of failure behavior at the scale of the composite structure, an ’interface solid element’ technique is used to consider localized cracking. Selected numerical and semi‐analytical results together with experimental validations are provided. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
About an analytical approach to a quasicontinuum method via Γ‐convergence
Authors: Schäffner Mathias , Schlömerkemper Anja
Published: October 2016

We report on an analytical study of a quasicontinuum method in the context of fracture mechanics in a one‐dimensional setting. To this end, we compare the asymptotic behaviour of a discrete model with pairwise interactions of Lennard‐Jones type and its quasicontinuum approximation via Γ‐convergence. In an elastic regime the limiting behavior of the orginal model and its quasicontinuum approximation coincide. In the case of fracture it turns out that it is necessary to coarse grain the quasicontinuum approximation in the continuum region and at the atomistic/continuum interface in order to capture the same behavior as the atomistic model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Assembly and Solution of the High‐Fidelity Generalized Method of Cells with Interface Damage
Authors: Schmerbauch Mario , Matzenmiller Anton
Published: October 2016

The assembly of the system of equations and its solution are presented for the High‐Fidelity Generalized Method of Cells (HFGMC) with interface damage. The direct stiffness assembly, which is used in the Finite Element Method with its unknown nodal displacements, is applied to the HGFMC. The nonlinear set of equations due to damage is solved with Newton's Method for the microscopic surface‐averaged displacements, which are the unknowns in the efficient version of the HFGMC. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient Simulation of Short Fibre Reinforced Composites
Authors: Springer Rolf , Meyer Arnd
Published: October 2016

In this paper we present a way how short fibre reinforced composites, produced by injection moulding, can be simulated in a linear thermoelastic setting, with an instationary heat equation. The main problem is the unknown stochastic fibre orientation. The only information known about this orientation field are the first moments of its distribution. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of the string method to compute minimum energy paths for a chain of bi‐stable elements using the finite element method and molecular dynamics
Authors: Ulz Manfred
Published: October 2016

Activated processes are frequently found in solid state mechanics. The energy landscape of such processes show a non‐convex behaviour, and therefore the computation of energy barriers between two stable minima is of importance. Such barriers are revealed by computing minimum energy paths. The string method is a simple and efficient algorithm to move curves over an energy landscape and to identify minimum energy paths.

A hierarchical two‐scale model recently introduced to the literature (molecular dynamics coupled with the finite element method) is used in this paper to investigate the string method in a model phase transition in a copper single crystal. To do so, bi‐stable elements are constructed and the energetic behaviour of a two‐elements chain is investigated. We identify successfully the minimum energy path between two local stable minima of the chain and demonstrate thereby the performance of the string method applied to a complex multiscale model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Double Grid Integration with Projection (DoGIP): Application to numerical homogenization by Fourier‐Galerkin method
Authors: Vondřejc Jaroslav
Published: October 2016

In this contribution, the DoGIP approach is introduced as a method for decomposition of a linear system into a (block) diagonal matrix based on a double grid integration and an interpolation/projection operator that is never assembled but optimised for fast matrix‐vector multiplication. The method reduces memory requirements, especially when higher order basis functions are used for discretisations. The method is explained for Fourier‐Galerkin method within a numerical homogenisation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Relating DEM contact parameters to macroscopic material parameters
Authors: Wessels Nicola , Hackl Klaus
Published: October 2016

Although the Discrete Element Method (DEM) is already widely applied in several fields of applications, one main challenge remains to define contact parameters that lead to realistic material behaviour. Here, it is shown how potentials can be defined on the contact level and from these a correlation to the macroscopic continuum parameters can be established. The analytically formed predictions are then compared to the results of discrete element simulations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)