bluuebunny/crossref_metadata_2025 huggingface dataset:
The Vibrational Behavior of Coupled Bladed Disks with Variable Rotational Speed
Authors: Kaptan Ferhat , Panning‐von Scheidt Lars , Wallaschek Jörg
Published: October 2015

Low pressure steam turbine blades are subjected to high static and dynamic loads during operation. These loads strongly depend on the turbine's rotational speed, leading to entirely new load conditions. To avoid high dynamic stresses due to the forced vibrations, a coupling of the blades, such as shrouds or snubber coupling, is applied to reinforce the structure. In this work the influence of the rotational speed on the vibration behavior of shrouded blades is investigated. Two fundamental phenomena are considered: the stress stiffening and the spin softening effect. Both effects are caused by centrifugal forces and affect the structural mechanical properties, i.e. the stiffness matrix K, of the rotating system. Since the rotational speed Ω appears quadratically, it is possible to derive the stiffness matrix as a second order matrix polynomial in Ω2 [3].

In the case of shrouded blades, contact forces between neighboring blades must be taken into account. The contact status and the pressure distribution in particular is strongly influenced by the rotational speed, respectively, centrifugal forces, caused by the untwisting and radial deformation of the blades. For the calculation, a three dimensional structural mechanical model including a spatial contact model is considered. The solution of the nonlinear equations of motion is based on the well known Multiharmonic Balance Method [2]. Here, the nonlinear forces are computed in the time domain and transferred in the frequency domain by the use of the Fast Fourier Transformation (FFT), also known as the Alternating Frequency Time method (AFT) [1]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multi‐mode model of a piezomagnetoelastic energy harvester under random excitation
Authors: Lentz Lukas , von Wagner Utz
Published: October 2015

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

Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive Fuzzy Sliding Mode Controller and Observer for a Dive Cell
Authors: Bessa Wallace M. , Kreuzer Edwin , Krumm Ludwig , Pick Marc‐André , Solowjow Eugen
Published: October 2015

We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
One‐dimensional simulation of the creep behavior of directionally solidified NiAl‐9Mo
Authors: Albiez Jürgen , Sprenger Ioannis , Heilmaier Martin , Böhlke Thomas
Published: October 2015

The directional solidification (DS) of the eutectic alloy NiAl‐9Mo (at. %) leads to a formation of single‐crystal molybdenum‐rich fibers embedded in a NiAl matrix and has promising high‐temperature properties. Material models describing each phase are necessary to be able to predict the materials behavior of the in‐situ composite under several conditions. Using a one‐dimensional Voigt‐Taylor model based on a phenomenological approach, the creep behavior is simulated and the results are compared to experimental data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A geometrical approach to remove stress singularities in continuum models of multi‐material structures
Authors: Blech Christopher , Falkenberg Paul , Langer Sabine C. , Vietor Thomas
Published: October 2015

In the frame of stress based topology optimisation multi‐material structures are investigated. At the interface of dissimilar materials an adhesive joint shall be considered. Selecting a continuum approach to model the two adherends and the adhesive, stress singularities occur at the material‐interfaces due to the difference in the impedance [1].

This contribution investigates a geometrical opportunity to remove singularities at the interface of two different linear elastic structures. Sensitivities of important parameters are qualitatively shown by a simple example consisting of two cubes under tension. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Characterization of Ni/Al hybrid foam from atomic to microscale
Authors: Chen Zhaoyu , Jung Anne , Heinze Stephan , Düster Alexander , Diebels Stefan
Published: October 2015

In this paper, the Ni/Al hybrid open‐cell foams are characterized on different hierarchical levels by means of experiments and numerical modeling from the atomic to the microscale. In this case, it is possible to compare the elastic‐plastic behavior at different scales in order to attain a deeper understanding of the multiscale properties of the Ni/Al hybrid foams. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled phase‐field – Cahn‐Hilliard model for lower bainitic transformation
Authors: Düsing Martin , Mahnken Rolf
Published: October 2015

The lower bainitic transformation is highly dependent on carbon diffusion. Bainite consists of bainitic ferrite, residual austenite and carbides. The numerical modeling of the interaction between these phases and the carbon is extremely demanding. The goal of this work is to describe the formation of carbides in lower bainite. To model the evolution of a bainitic sheaf a phase‐field model is coupled with a Cahn‐Hilliard equation simulating the diffusion. The system of equations is solved using the finite element method. Numerical examples show the growth of the ferrite and the following uphill diffusion within this phase. At accumulation points of carbon, carbides are precipitated. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An atomistic scale analysis of ferroelectric nanodomain interfaces
Authors: Endres Florian , Steinmann Paul
Published: October 2015

We discuss numerical results of nanodomain interfaces using a new extended molecular statics algorithm for ferroelectric materials. The new algorithm is able to not only calculate the change of the polarization behavior caused by strain but also the influence on the polarization behavior due to mechanical stress. The size effects of 180° head to head and tail to tail nanodomains have already been investigated. This study also considers 90° domain walls and discusses the impact of mechanical stress on polarization patterns and system energies of nanodomain interfaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An Intrinsic Geometric Formulation of the Equilibrium Equations in Continuum Mechanics
Authors: Eugster Simon R.
Published: October 2015

The theory of invariant continuum mechanics is based on the concept that forces and stresses are defined as elements of the cotangent bundle of the configuration manifold. While body and physical space are modeled as differentiable manifolds, the infinite dimensional configuration manifold is given by all configurations of the body in the physical space. In this paper a virtual work principle is postulated which leads together with an induced traction stress and Stokes' theorem directly to the local equilibrium equations and the traction boundary conditions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal bounds from below of the critical load for elastic solids subject to uniaxial compression
Authors: Castellano Anna , Foti Pilade , Fraddosio Aguinaldo , Marzano Salvatore , Piccioni Mario Daniele
Published: October 2015

In the recent papers [1,2] we studied a new procedure based on the Korn inequality for determining sufficient conditions for the Hadamard stability, aimed at determining optimal lower bound estimates for the critical load in bifurcation problems. Here, we discuss the effectiveness of our approach for the classical representative problem of uniaxial compression of a Mooney‐Rivlin circular cylinder. We find that our lower bound estimate is effective and advantageous for applications, since it is easily implementable in numerical codes. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On fast and accurate modelling of distributed fibre directions in composites
Authors: Goldberg Niels , Ihlemann Jörn
Published: October 2015

This contribution presents an alternative approach for the consideration of distributed fibre directions in a composite, which is almost as accurate as the solution of angular integrals but considerably faster. It makes use of representative directions according to an Angular Central Gaussian distribution function and does not require the solution of angular integrals. As the choice of the representative directions bears a significant impact on the accuracy of the method, a study on the integration error is presented. Furthermore, the results of homogeneous deformations using the already existing methods as well as the new approach are compared to each other, pointing out the advantages and disadvantages of each method. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling the evolution of microstructures in finite plasticity
Authors: Günther Christina , Junker Philipp , Hackl Klaus
Published: October 2015

Kochmann and Hackl introduced in [1] a micromechanical model for finite single crystal plasticity. Based on thermodynamic variational principles this model leads to a non‐convex variational problem. Employing the Lagrange functional, an incremental strategy was outlined to model the time‐continuous evolution of a first order laminate microstructure. Although this model provides interesting results on the material point level, due to the global minimization in the evolution equations, the calculation time and numerical instabilities may cause problems when applying this model to macroscopic specimens.

In order to avoid these problems, a smooth transition zone between the laminates is introduced to avoid global minimization, which makes the numerical calculations cumbersome compared to the model in [1]. By introducing a smooth viscous transition zone, the dissipation potential and its numerical treatment have to be adapted. We obtain rate‐dependent time‐evolution equations for the internal variables based on variational techniques and show as an example single slip shear. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical analysis of Ni/Al hybrid metal foams using the finite cell method
Authors: Heinze Stephan , Chen Zhaoyu , Jung Anne , Diebels Stefan , Düster Alexander
Published: October 2015

Aluminium metal foams are a new type of material that can be used in many lightweight applications. One method to improve their mechanical properties is to coat them with a thin layer of nickel by electrodeposition. A voxel representation of this hybrid foam can be obtained in a straightforward way using a CT scanner. The voxel‐based geometry can then be processed and modified with respect to the thickness of the nickel layer in order to investigate its influence on the effective properties. By employing the finite cell method (FCM) we are able to automatically convert the voxel‐based geometry into a finite cell grid and to directly perform a homogenization procedure. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the natural Fiber (Maize) Composite material
Authors: Ilie Ruxandra , Chiroiu Veturia
Published: October 2015

This work is focused on the compressive behavior in the elastic region of a composite material made out of stalk‐based maize fiber and unsaturated polyester resin polymer as matrix with methyl ethyl ketone peroxide as a catalyst and Cobalt Octoate as a promoter [1]. Deformation and fracture behavior are investigated by using Extended Finite Element Method (XFEM). XFEM enables the accurate approximation of solutions with jumps, discontinuities or general high gradients across interfaces between the fibers and the matrix [2], [3]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The perturbation method applied to tube drawing with floating plug
Authors: Ioan Rodica , Ioan Stefan
Published: October 2015

The determination of the load on the machine tool is crucial in the mechanics of metal forming processes as it has a critical influence over the deformation of the material into a new shape and the optimal conditions for the process. The problems of strip, wire, tube drawing without plug, tube drawing with floating plug [1‐4] viscoplastic deformation has no exact solutions, but this paper addresses them using an approximate method. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Rank‐One Convexification Approach for the Modeling of Magnetic Shape Memory Response
Authors: Buckmann Karsten , Kiefer Björn , Bartel Thorsten , Menzel Andreas
Published: October 2015

We present an incremental energy minimization model for magnetic shape memory alloys (MSMAs) whose derivation departs from the constrained theory of magnetoelasticity [1], but additionally accounts for elastic deformations, magnetization rotation, and dissipative mechanisms. The minimization of the proposed incremental energy yields the evolution of the internal state variables. In this sense, the presented modeling concept clearly distinguishes itself from standard phenomenological approaches to MSMA modeling [4]. The extended model is applied to simulate the response of single crystalline Ni2MnGa. It is shown to accurately capture the nonlinear, anisotropic, hysteretic, and highly stress level‐dependent features of MSMA behavior, based on just a few fundamental material parameters, which is validated by comparison to experimental data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Direct connection of rheological elements at large strains: Application to multiplicative viscoplasticity
Authors: Kießling Robert , Landgraf Ralf , Ihlemann Jörn
Published: October 2015

In the field of nonlinear continuum mechanics, rheological models are often used to exemplify the structure of complex material models at large strains. For this purpose, different rheological elements are combined in series and parallel connections. Ihlemann [1] developed an innovative concept, which enables the direct connection of rheological elements within the framework of multiplicative decomposition of the deformation gradient. In the contribution at hand, this approach is applied to multiplicative viscoplasticity. Towards this end, the relations for parallel and series connections are introduced and several individual material models, i.e. the rheological elements, are defined. By analytical and numerical evaluation of the connection relations, a viscoplastic material model from the literature is reproduced. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Determination of material parameters of heterogeneous viscoelastic curing polymers
Authors: Klinge Sandra , Steinmann Paul
Published: October 2015

Two goals characterize the present contribution: First, the development of a numerical approach for determining the properties of the material microstructure, and second, the shift of the focus of the inverse analysis from investigating a purely elastic material toward the parameter identification related to heterogeneous inelastic materials. As a rule, the constitutive laws in this case involve a greater number of material parameters the determination of which requires different kinds of tests. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Phase‐field modeling of martensitic phase transformations in polycrystals coupled with crystal plasticity – A spectral‐based approach
Authors: Kochmann Julian , Wulfinghoff Stephan , Svendsen Bob , Reese Stefanie
Published: October 2015

The purpose of this work is the phase‐field modeling of fcc‐to‐bcc martensitic phase transformations in polycrystals and the coupling with crystal plasticity. Assuming microscopic periodic fields, Green‐function‐ and fast Fourier transform (FFT)‐methods are used to solve the quasi‐static balance of linear momentum. The Allen‐Cahn evolution equation is discretized based on a semi‐implicit time integration scheme in Fourier space. Two‐dimensional results are presented and the interplay between martensitic phase transformation and plastic slip is studied at different stages of the deformation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dislocation Structure of Grain Boundaries in Single Crystals Deforming in Simple Shear
Authors: Koster Michael , Le Khanh Chau
Published: October 2015

A model for the formation of grain boundaries in single crystals having a single active slip system for the case of plane strain simple shear is proposed. It is shown that non‐convexity of the condensed energy gives rise to the formation of a laminate structure, where sharp interfaces between laminate layers are interpreted as grain boundaries. Based on these results the dislocation structure of the boundaries is determined introducing a transition zone between laminate layers, where smooth functions of displacement and plastic slip connect adjacent layers. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Phenomenological modelling for viscohyperelasticity: How to find suitable evolution laws in order to extend hyperelastic models?
Authors: Kröger Nils Hendrik , Juhre Daniel
Published: October 2015

Materials used for adhesive tapes indicate viscohyperelastic behaviour. We presented a model approach for extending hyperelastic material models for viscous effects via an evolution law approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of Carbon Fiber Reinforced Plastics for Wave Propagation Analysis in Plates
Authors: Lammering Rolf , Hennings Bianca
Published: October 2015

The modeling of the carbon fiber reinforced plastic (CFRP) for finite element analysis of wave propagation in plates from this material is presented. The random distribution of fibers in the matrix material is considered in a microscale model in order to properly capture the experimentally observed “quasi‐continuous mode conversion” (QCMC). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of micro cutting considering crystal plastic deformations
Authors: Lohkamp Richard , Kuhn Charlotte , Müller Ralf , Aurich Jan C. , Schneider Frank
Published: October 2015

The micro cutting process of microstructured material is simulated with consideration of the heterogeneities of the microstructure. In the case of cp‐titanium with its hcp crystal structure the basal and prismatic slip systems are taken into account. The concept of crystal plasticity for large deformations is applied considering elastic anisotropy, self and latent hardening. The visco‐plastic evolution law incorporates rate dependent material behavior. This setup is implemented within the finite element method. The effects of the microstructure are demonstrated by an illustrative example and a comparison to an isotropic von Mises elasto‐plastic material. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the sonic composites with scatterers made from auxetic material
Authors: Mo¸ snegu¸ tu Valerica , Donescu Stefania
Published: October 2015

A finite size periodic array of resonators made from auxetic material embedded into an epoxy matrix is analyzed in this paper. According to the Bragg's theory, the sound attenuation band is due to the superposition of multiple reflected waves inverse proportional to the central distance between resonators. The sound attenuation in such composites is studied using a method that combines the features of the cnoidal method and the genetic algorithm [1‐3]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of imperfect contact interfaces in sonic composites
Authors: Munteanu Ligia , Brişan Cornel
Published: October 2015

In this paper, the tangential and normal discontinuities at the interface between the scatterer and the matrix are independently modeled, and these relative displacements are directly proportional to the corresponding components of tractions at the interface. The generation of full band‐gaps is investigated on the basis of the derived imperfect interface conditions for a sonic plate with an array of acoustic piezoceramic hollow spheres scatterers embedded in an epoxy matrix. The scatterers are made from functionally graded materials with radial polarization. Numerical evaluation has shown that imperfect interface may have a significant effect on the increasing of the length of the full band‐gaps. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Modeling of Functional Fatigue in NiTi Wires
Authors: Osman Muhammad , Bartel Thorsten , Menzel Andreas
Published: October 2015

Motivated by the high potential of shape memory alloys (SMA) in several industrial applications, we investigate the material response under cyclic loading. In particular, the focus is set on the modelling of functional fatigue, which results in the deterioration of the specific features of SMA. In fact, functional fatigue restricts SMA in terms of its applicability for real structures and workpieces. This necessitates the development of material models which take this phenomenon into account. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A misorientation dependent grain boundary yield criterion
Authors: Prahs Andreas , Bayerschen Eric , Böhlke Thomas
Published: October 2015

An equivalent plastic strain gradient theory, cf. [1], is extended by a GB flow rule, that accounts for the misorientation of adjacent grains. In contrast to previous works, the grain boundary (GB) resistance against plastic flow is not treated as a constant parameter. Therefore, in the work at hand, the grain boundary dislocation density (GBD), cf. [2], is used as a measure for geometrical mismatch between all glide system orientations of two adjacent grains. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Constitutive modeling of fiber‐reinforced aerogels
Authors: Rege Ameya , Itskov Mikhail
Published: October 2015

Aerogels are open‐cell highly porous solids having exclusive properties such as lowest bulk density, lowest thermal conductivity and lowest acoustic velocity. These properties make them useful over a large spectrum of applications. However, their brittle and hydrophilic natures result in a road block which is overcome by polymer or fiber reinforcement. In this study, we are focussing on fiber‐reinforced aerogels which retain the exclusive properties of aerogels mentioned above while giving them a good load bearing strength at the same time. These fiber‐reinforced aerogels show many complex phenomena under loading such as, a strong nonlinearity, cyclic stress softening, and permanent set. However, there have been very few studies on fiber‐reinforced aerogels oriented towards their mechanical characterization. To the best of our knowledge, there also is no micromechanical model that can capture the constitutive response of these fiber‐reinforced aerogels. In this contribution, we propose a micro‐mechanically motivated constitutive model of fiber reinforced aerogels. The prime source of elasticity and damage in these aerogels is the effect of bending and breakage of fibers in the material network. Accordingly, we consider non‐linear bending of fibers supported by an elastic foundation of particles. Based on this concept, the strain energy function is analytically derived for a single fiber in a particular direction. The strain energy of the whole network is then obtained by integration over an unit sphere. The model shows good agreement with experimental data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Characterization of short fiber reinforced polymers
Authors: Röhrig Céline , Diebels Stefan
Published: October 2015

This contribution presents ideas, how composite materials can be characterized with respect to experimental testing. The material properties of the investigated short glass fiber reinforced polymer are obtained by providing results from the experiment in order to seperate different material effects, such as elasticity, plasticity, damage, viscoelasticity, compressibility and anisotropy. Therefore, at first, linear uniaxial tensile tests with cyclic loadings have been realized. The application of the material in this work is the machining by a three‐dimensional forming process. Hence, multiaxial loadings have to be additionally taken into account matching these conditions. In order to provide more information, biaxial tensile tests have to be realized using a testing device supplying the additional necessary experimental data [1, 2]. A final aim of this work is to develope a verification experiment representing the three‐dimensional forming process as realistically as possible, e. g. a Nakajima test [4]. For this case, a three‐dimensional optical analysis in order to get the necessary measurement data, is indispensable to realize an inverse method [3] by comparing the information of the complete deformation field as well as the force data of the experiment using a given material model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Characterisation of filled rubber with a pronounced non‐linear viscoelasticity
Authors: Scheffer Tobias , Goldschmidt Florian , Diebels Stefan
Published: October 2015

This contribution presents the characterisation of an incompressible carbon black‐filled elastomer as one characteristical example for highly filled rubber. It shows a strongly pronounced non‐linear viscoelastic behaviour and the most important characteristic is the extremely long relaxation time which has to be taken into account. The material model is developed with respect to uniaxial tension data. The basis in the development of a phenomenological model is given by the basic elasticity. For this evaluation the long term relaxation behaviour results in a complex experimental procedure. Therefore, special attention has to be paid according to an optimised experimental process in order to get the necessary reference data in an adequate and reproduceable way [1].

With this model basis further investigations are taken into account concerning the time‐dependent viscoelasticity. Therefore, cyclic deformations from zero up to a maximum of deformation are considered for different strain rates. Furthermore, the relaxation behaviour is investigated for multiple strain levels. The phenomena which are observed in the experimental results yield in a purely viscoelastic model, based on a rheological analogous model consisting of an equilibrium spring and several Maxwell‐elements which contain nonlinear relations for the relaxation times of the dashpot elements [1,2].

The material model's numerical realisation is accomplished in two ways. Because of its numerical simplicity especially according to the parameter identification the model is restricted only to the simple case of uniaxial tension. A second, alternative implementation is executed providing the benefit that more complex deformation conditions can also be taken into account. Therefore, the general, three‐dimensional finite model is implemented in an open‐source Finite Element library [3]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Inverse Parameter Identification for Orthotropic Elasto‐Plastic Sheet‐Steel
Authors: Söhngen Benjamin , Willner Kai
Published: October 2015

In this contribution the Finite Element Model Updating (FEMU) approach is utilized to determine the material parameters of sheet‐steel. From experimental testing it is observed that the considered cold‐rolled steel exhibits orthotropic behaviour. To regard this in the simulation, a user‐implemented material model based on a quadratic yield function is used. Via the method of digital image correlation (DIC), the displacement field of a biaxially loaded specimen is measured from images taken at different stages of loading. Comparing the experimentally determined displacements to those obtained by simulation an error measure is defined which can be minimized by optimization algorithms. Starting with initial values for the orthotropic elasto‐plastic material parameters, the FEM model is thus updated consecutively until a specified error margin is reached. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
External boundary value problems of steady vibrations in the theory of rigid bodies with a double porosity structure
Authors: Svanadze Merab
Published: October 2015

This paper concerns with the linear 3D theory of rigid solids with a double porosity structure. Basic external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for regular (classical) solutions of these BVPs are established. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Automatic Implementation of Elasto‐plastic Incremental Formulations at Finite Strains using Hyper‐Dual Numbers
Authors: Tanaka Masato , Balzani Daniel , Schröder Jörg
Published: October 2015

Numerical simulation of standard dissipative materials undergoing finite strains remains an important and challenging topic in computational mechanics. The incremental variational formulation (IVF), firstly proposed by Ortiz et al. [1], provides a general variational framework which is suitable for the implementation of a broad range of constitutive laws for standard dissipative materials. The IVF recasts the inelasticity theory as an equivalent optimization problem where the incremental stress potential is minimized with respect to the internal variables. However, their implementation often requires more effort than classical formulations due to high‐order tensor derivatives. In this contribution, a novel implementation of IVFs is presented to arrive at a fully automatic and robust scheme with computer accuracy using hyper‐dual numbers (HDNs). The HDNs, which are originally developed by Fike [2], derive exact and automatic derivative calculations without any cumbersome choice of perturbation values. Its uncomplicated implementation for associative finite strain elasto‐plasticity and its performance is illustrated by a representative numerical example. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A micromechanical model for the transformation induced plasticity in polycrystalline steels
Authors: Waimann Johanna , Junker Philipp , Hackl Klaus
Published: October 2015

Due to the effect of transformation induced plasticity (TRIP) , TRIP‐steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the volume fractions of the single phases, the plastic strain and the hardening parameter in every grain of the polycrystalline material as internal variables. Furthermore, we apply the Principle of the Minimum of the Dissipation Potential to derive the associated evolution equations. The use of a coupled dissipation functional and a combined Voigt/Reuss bound directly results in coupled evolution equations for the internal variables and in one combined yield function. Additionally, we show numerical results which prove our model's ability to give a first prediction of the TRIP‐steels' complex material behavior. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermoplastics under Long‐Term Loading: Experiments and Viscoelastic‐Viscoplastic Modeling
Authors: Zerbe Patrick , Schneider Benjamin , Moosbrugger Egon , Kaliske Michael
Published: October 2015

The behavior of polyoxymethylene, a semicrystalline thermoplastic, with respect to mechanical long‐term loads is studied. Experiments demonstrate the creep behavior for constant load and also for cyclic unloading. The latter shows partial time‐dependent strain recovery during unloading and an extended lifetime. Based on the experimental results, a viscoelastic‐viscoplastic‐damage material model for finite strains is proposed. Numerical simulations are compared to the experimental results demonstrating the model's capabilites and limitations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear numerical simulation of ferroelectric‐ferromagnetic multifunctional composites
Authors: Avakian Artjom , Ricoeur Andreas
Published: October 2015

The theoretical background of nonlinear constitutive multifield behavior is presented. Nonlinear material models describing the ferroelectric or ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of the nonlinear magnetostrictive and ferroelectric behaviors. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic respectively magnetostrictive phases are simulated and the resulting effects analyzed. The developed tools enable the prediction of the electromagnetomechanical properties of smart multiferroic composites and supply useful means for their optimization. Goals are to improve the efficiency of ME coupling and to reduce damage associated with the poling process. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Correction of Characteristics of Subsystems of Torsionally Vibrating Complex Mechatronic Systems as an Introduction to Solution of Their Inverse Task
Authors: Buchacz Andrzej
Published: October 2015

In this paper the analysis of torsionally vibrating subsystem of complex mechanical and mechatronic systems by using the the exact and approximate methods were the main purposes to solve the task of assignment of frequency‐modal analysis and characteristics of mechatronic system. The characteristic of the elementary subsystems using the exact and approximate methods has been determined according to accepted frequencies and the correction coefficient. The frequencies were chosen from the spectrum in which the synthesis of complex systems will be conducted. It is very important that the difference of flexibility values in the spectrum was minimal. The coefficient of the correction has been determined according to the flexibility values of chosen points and it is equal to quotient of flexibility calculated using the exact method across the flexibility delivered by using the approximate method. The coefficient of the correction is the zero‐dimensional quantity. After determination of the correction coefficient the medium value which has been afterwards considered in correlation of dynamic characteristics has been calculated. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Intrinsic symmetries in constitutive modeling of magneto–elastic materials
Authors: Dobovšek Igor
Published: October 2015

We consider a class of non‐dissipative materials whose constitutive equations are derived from a suitably constructed thermodynamic potential function. The Gibbs energy relation is introduced as a function of stress, strain, magnetic field, magnetization, and temperature. By minimization with respect to the chosen subset of independent variables we derive the corresponding set of constitutive equations. The chosen form of the free energy function leads to the linear elastic and nonlinear ferromagnetic coupling where non‐linearity emerges in terms associated with the strength of magnetization. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application and modification of the POD method and the POD‐DEIM for model reduction in porous‐media simulations
Authors: Fink Davina , Ehlers Wolfgang
Published: October 2015

Researchers with a continuum‐mechanical background typically use a multi‐phasic and multi‐component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuum‐mechanical manner and solved using the finite‐element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model‐reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of proper‐orthogonal decomposition (POD) for linear problems and the discrete‐empirical‐interpolation method (DEIM) in combination with the POD method (POD‐DEIM) for nonlinear problems are investigated. Using the POD method, a given data set is approximated with a low‐dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre‐computation in the full (unreduced) system in each time‐step (so‐called “snapshots” of the system). Dealing with porous‐media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non‐negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of Vortex‐Induced Oscillations within a Shear Thinning Liquid
Authors: Gundlach Janto , Schlosser Alexander , Wünsch Olaf
Published: October 2015

The present work discusses the impact of nonlinear shear thinning in a viscous fluid flow on the vibration behavior of an elastic bar. In the process numerical simulations have been performed concerning a well‐known FSI benchmark geometry. In contrast to past investigations a non‐Newtonian liquid of the Carreau‐Yasuda type is used as fluid component. In order to accomplish the coupling between the liquid and the solid domain, an approach using quasi‐Newton iterations is applied. In a parameter study material and geometrical parameters are changed. The solutions show distinct deviations compared to results obtained with a Newtonian liquid. These differences emphasize the nonlinearity of the shear thinning material model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling a Halfspace with Tunnel using a Coupled Integral Transform Method – Finite Element Method Approach
Authors: Hackenberg Manuela , Müller Gerhard
Published: October 2015

Vibrations that are excited by moving trains inside a tunnel are regularly transmitted via the tunnel and the surrounding soil and often perceived at the surface. In order to assess the effects of the arising vibrations and to be able to model possible mitigation measures, a suitable model of the system is necessary. In this paper, a coupled approach is presented, where the emission system of an underground tunnel is modeled using the Finite Element Method while the transmission medium of the soil is described by Integral Transform Methods. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermo‐mechanical modelling of cellular ceramic composites by a multiphase approach of porous media
Authors: Jung Anne , Diebels Stefan
Published: October 2015

Refractory materials have a wide range of applications in the steel‐making industry for example as lining of furnaces, oxygen converters or for ladles. Often, magnesia carbon bricks (MgO‐C) are used. These are made of a periclase phase (MgO) with carbon inclusions and pores. In their applications, refractories are subjected to thermal and mechanical loads causing damage. The thermo‐mechanical behaviour of MgO‐C composites and hence their thermal stability could be improved significantly using cellular MgO‐C composites based on carbon foams [1, 2]. The present contribution focuses on the development of a fully coupled phenomenological thermo‐mechanical continuum model based on the theory of porous media (TPM) with a new kinematic coupling of the displacement field of all constituents. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling, Simulation and Parameter Identification for Rate‐Dependent Magnetoactive Polymer Response
Authors: Kiefer Bjoern , Haldar Krishnendu , Menzel Andreas
Published: October 2015

A finite deformation framework for nonlinear magneto‐viscoelasticity is introduced and applied to the constitutive and structural modeling of magnetoactive polymer (MAP) response. In this thermodynamically‐consistent formulation the free energy function consists of purely elastic, purely magnetic and coupling contributions, where the rate‐dependence is fully attributed to the non‐magnetizable matrix material. The model consistently accounts for saturation in the magnetic as well as the magnetostrictive behavior. The identification of material parameters from experimental data is briefly described. Finally, a finite element model for the large strain magneto‐mechanical problem is established and tested considering MAP behavior. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A constitutive and damage model for high cycle fatigue of tetragonal ferroelectrics
Authors: Lange Stephan , Ricoeur Andreas
Published: October 2015

Reliability and life time of smart materials are crucial features for the development and design of actuator and sensor devices. Being widely used and exhibiting brittle failure characteristics, ceramic ferroelectrics are of particular interest in this field. Due to manifold interactions of the complex nonlinear constitutive behavior on the one hand and the damage evolution in terms of microcrack growth on the other, modeling and simulation are inevitable to investigate influence parameters on strength, reliability and life time. A condensed approach is used for the simulations considering just one characteristic point in the material, nonetheless accounting for polycrystalline grain interactions. On this basis, a model to predict the life time in terms of high cycle fatigue under electromechanical loading conditions is introduced. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hydroelastic stability of multi‐plate structures interacting with flowing fluid
Authors: Bochkarev Sergey , Lekomtsev Sergey , Matveenko Valery
Published: October 2015

The paper is concerned with the finite‐element analysis of natural vibrations and hydroelastic stability of two parallel plates interacting with liquid. The influence of the fluid layer thickness on the eigenfrequencies, vibration modes and hydroelastic stability boundary are estimated based on the results of numerical solution of some example problems. The numerical investigation substantiates the existence of various instability modes, the onset of which depends on the combinations of kinematic boundary conditions specified at the plate ends. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shock structure for macroscopic multi‐temperature model of binary mixtures: comparison with kinetic models
Authors: Madjarević Damir
Published: October 2015

The present study deals with the shock wave profiles in the macroscopic multi‐temperature (MT) model of binary gaseous mixtures. For that purpose we have adopted the hyperbolic model developed within the framework of extended thermodynamics [1] in which we include viscosity and thermal conductivity to eliminate restriction on parameters. This allows us to compare our results with more sophisticated kinetic solutions, which were computed for hypothetic mixtures of gases [2]. Numerical implementation of the MT model is considerably simpler than the one for Boltzmann equations for mixtures or the direct simulation Monte Carlo method (DSMC). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reduction Approaches for Thermogasdynamic Lubrication Problems
Authors: Mahner Marcel , Lehn Andreas , Schweizer Bernhard
Published: October 2015

Gas thrust bearings are often used in low‐load applications, e.g. in air cycle machines, in micro gas turbines or in rotor systems for fuel cell applications, to support a shaft in axial direction. The pressure and temperature distribution in a gas thrust bearing pad are described by the generalized Reynolds equation according to Dowson and the 3D energy equation. In this paper, two different approaches are presented in order to reduce the dimension of the governing nonlinear integro‐differential equation system and in order to stabilize the solution process. In the first reduction approach, the temperature in the fluid is averaged across the fluid film according to Lee and Kim. In the second approach, Legendre polynomials are used to approximate temperature, density and fluidity across the fluid film according to Elrod, Brewe and Moraru. The reduction techniques are compared with respect to numerical efficiency, accuracy and convergence behavior. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of electrodynamic‐mechanical coupling phenomena in smart magnetoelectroelastic materials
Authors: Merkel Eugen , Ricoeur Andreas
Published: October 2015

The coupling of electric, magnetic and mechanical phenomena may have various reasons. The famous Maxwell equations of electrodynamics describe the interaction of transient magnetic and electric fields. On the constitutive level of dielectric materials, coupling mechanisms are manyfold comprising piezoelectric, magnetostrictive or magnetoelectric effects. Electromagnetically induced specific forces acting at the boundary and within the domain of a dielectric body are, within a continuum mechanics framework, commonly denoted as Maxwell stresses. In transient electromagnetic fields, the Poynting vector gives another contribution to mechanical stresses. First, a system of transient partial differential equations is presented. Introducing scalar and vector potentials for the electromagnetic fields and representing the mechanical strain by displacement fields, seven coupled differential equations govern the boundary value problem, accounting for linear constitutive equations of magnetoelectroelasticity. To reduce the effort of numerical solution, the system of equations is partly decoupled applying generalized forms of Coulomb and Lorenz gauge transformations [1,2]. A weak formulation is given to establish a basis for a finite element solution. The influence of constitutive magnetoelectric coupling on electromagnetic wave propagation is finally demonstrated with a simple one‐dimensional example. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)