bluuebunny/crossref_metadata_2025 huggingface dataset:
Limit States in Alternately Loaded Plates
Authors: Todres Russell , Stoffel Marcus , Weichert Dieter
Published: November 2010

In the present study, a circular plate is inelastically deformed by uniform pressure, which is released and then alternately applied to the same peak level. For each iteration, snap‐through occurs at an increased pressure relative to the previous one, leading to additional inelastic deformation. At some point, either the plate fails or a limit state of deformation is reached under peak pressure without snap‐through. This phenomenon is studied experimentally and theoretically to determine the conditions under which the limit state is stable. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An improved Interior‐Point Algorithm for Large‐Scale Shakedown Analysis
Authors: Simon Jaan‐Willem , Weichert Dieter
Published: November 2010

This work focuses on the calculation of shakedown load‐factors of structures by using the lower‐bound theorem of shakedown analysis. The resultant optimization problem is solved by an interior‐point algorithm.

In general, the application of shakedown analysis to practical problems leads to large‐scale problems with large numbers of unknowns and constraints. Thus the solution turns out to be computationally intensive. For this reason it is important to reduce the dimension of the considered problem. Therefore, the major improvement of the presented algorithm consists of a problem‐oriented reformulation of the problem reducing the size of the system to be solved. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Higher Frequency of Free Vibrations of Thin Annular Plates Made of Functionally Graded Material
Authors: Wirowski Artur
Published: November 2010

Subject of this paper is a thin plate with a characteristic geometry: periodic in one direction and smoothly varying along the other. The aim of the contribution is to formulate and apply the averaged model which can describe higher frequencies of free vibrations. Problem of finding frequencies of free vibrations is very important. It could be applied to many engineering problems such as resonance phenomena, wave propagation, absorption of vibrations and many others. When the considered plate is made of an isotropic material, we can find the first, the second and the others frequencies in simply way. But if we consider plate made of a functionally graded material [1], which have varying properties and which is made of two components, this problem is more complicated. In this cause, apart from family of the base frequencies (first, second, etc), which depend on macroscopic properties of the plate, we have the higher frequency, which depends on a microscopic structure. We can find many papers describing the base frequencies of free vibrations for many different types of structures (for example [2] for considered type of plate). In this paper, we find the higher frequency. For solving this problem, we use the tolerance averaging technique described in [3]. This theory allows to take into account the microstructure size and to find the higher frequency of free vibrations. The equations have smooth coefficients. They can be solved numerically with help of the finite difference method, in polar coordinates for an annular plate. Next, we use special procedure for selecting of the higher frequencies of free vibrations, which depend on the microstructure size, from the list of all frequencies. After that we analyze an influence of ratios of material properties and the microstructure size on the higher frequency of free vibrations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reibungsdämpfung in ausgedehnten, verschraubten Fügestellen
Authors: Hölzl Johannes Sebastian , Sextro Walter
Published: November 2010

Bei der Konstruktion von Maschinen ist es oftmals erforderlich, Schwingungen minimal zu halten. Um z.B. die Lebensdauer zu erhöhen, Material einzusparen oder den Geräuschpegel gering zu halten muss oft ein großer Aufwand zur Dämpfung von auftretenden Schwingungen betrieben werden. In vielen technischen Anwendungen werden Einzelteile miteinander verschraubt. Diese Fügestellen können gezielt und mit wenig Aufwand zur Schwingungsdämpfung herangezogen werden. Die Berechnung des dynamischen Verhaltens verschraubter Strukturen stellt immer noch eine Herausforderung dar. Es wurde eine Methode entwickelt, um den eingeschwungenen Zustand elastischer, miteinander verschraubter Körper mit rauen Fügestellen bei periodischer Anregung zu berechnen. Als Basis dienen Finite Elemente Modelle der einzelnen Teile, deren Freiheitsgrade durch modale Kondensation reduziert werden. Unter Anwendung des Verfahrens von Ritz und Galerkin wird eine Näherungslösung für den eingeschwungenen Zustand des nichtlinearen, gekoppelten Systems ermittelt. Abhängig von den Schraubenvorspannkräften sowie den bestimmenden Parametern der Kontaktflächen, Rautiefe und Reibungskoeffizient, kann die Systemantwort berechnet und optimiert werden. Um die Berechnungsmethode zu verifizieren wurden Experimente durchgeführt. Der Vergleich zwischen Messung und Rechnung zeigt eine gute Übereinstimmung. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Integrodifferentialgleichungen in der Analyse innerer Dynamik von Planetengetrieben
Authors: Hortel Milan , Škuderová Alena
Published: November 2010

Genauere dynamische Analyse von hochtourigen Planetengetrieben führt auf mathematisch‐physikalische Modelle, deren Bewegungen bei Anwendung der Massendiskretisierung durch deterministische gewöhnliche nichtlineare zeitlich heteronome Differentialgleichungen beschrieben werden. Diese Systeme von n Freiheitsgraden können ein breites Spektrum von Eigenschaften aufweisen, das von regulären periodischen bis zu irregulären Lösungen vom chaotischen Charakter reicht. Zur dynamischen Analyse solcher komplizierter Systeme wurde ein sukzessives Approximationsverfahren der zur Differentialrandwertaufgabe äquivalenten Integrodifferentialgleichungen mit lösenden Kern in Form von einer Greenschen Resolvente angewendet. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of Dynamical Responses for the MDF Wooden Material
Authors: Litak Grzegorz , Scheffler Michael , Morgenstern Gunnar
Published: November 2010

The nonlinear analysis have been performed on the experimental data of a beam vibration composed of a wooden material MDF (Medium‐Density Fiberboard). Firstly, the beam was subjected to the harmonic excitation on the clamp with its first eigenfrequency. After reaching the eigenfrequency, the excitation was switched of and the velocity amplitudes were measured. To identify the frequencies and the damping of vibrations, we applied nonlinear methods including Hilbert transform and wavelets. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Solution of High Dimensional Fokker Planck Equations using Orthogonal Polynomial Expansion
Authors: Martens Wolfram , von Wagner Utz
Published: November 2010

Solving the Fokker‐Planck‐Equation for multidimensional nonlinear systems is a great challenge in the field of stochastic dynamics. As for many mechanical systems a general idea about the shape of stationary solutions for the probability density function is known, it seems promising to use an approach that contains this knowledge. This is done using a Galerkin‐method which applies approximate solutions as weighting functions for the expansion of orthogonal polynomials, e.g. generalized Hermite polynomials [1]. As examples, nonlinear oscillators containing cubical restoring (Duffing oscillators) and cubical damping elements are considered. The method is applied to the two‐dimensional problem of a single‐degree‐of‐freedom oscillator and consecutively extended up to dimension ten. Results for probability density functions are presented and compared with results from Monte Carlo simulations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear Behavior of Piezoceramic Actuators
Authors: Nguyen Huy The , von Wagner Utz
Published: November 2010

Nonlinear behavior of piezoceramics is a well‐known phenomenon. For large stresses and/or strong electric fields it is described by various hysteresis curves. Quasi‐static experiments exhibited hysteresis relations between excitation voltage and strain as well as between excitation voltage and electric displacement. This behavior can be modeled by using the classical Preisach model. On the other hand, typical nonlinearities of Duffing type such as jump phenomena, multiple stable amplitude responses at the same excitation voltage and frequency, and the presence of superharmonics in response spectra can be observed when piezoceramic actuators are excited near resonance, even at weak electric fields. In this paper, different experimental results for both quasi‐static and dynamic nonlinear behavior and corresponding models are presented and compared. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nichtlineares Kontaktmodell für die Schleif‐Prozess‐Simulation
Authors: de Payrebrune Kristin M. , Kröger Matthias
Published: November 2010

Die Herstellung von Hochleistungswerkzeugen aus Hartmetall, wie Bohrern oder Schaftfräsern, ist sehr aufwändig und aufgrund der hohen Härte des Materials nur durch Schleifprozesse realisierbar. Um den Schleifprozess zu optimieren ist die Simulation der Schwingungen während des Prozesses in den Fokus der Wissenschaft gerückt. Besonders die Wechselwirkungen zwischen Werkstück, Schleifprozess und Maschinenstruktur werden in diesem Zusammenhang eingehend untersucht, da sie die Qualität der Werkstücke beeinflussen.

Um die Prozess‐Struktur‐Wechselwirkungen, hervorgerufen durch den nichtlinearen Kontakt zwischen Schleifscheibe und Werkstück, zu untersuchen werden am Institut für Maschinenelemente, Konstruktion und Fertigung grundlegende Analysen von Schleifprozessen durchgeführt und die Ergebnisse in einen Modellierungsansatz für diese Fertigungsprozesse implementiert. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Active Vibration Control of Roll Press System by Piezoelectric Actuators
Authors: Töhönen Mika , Seemann Wolfgang
Published: November 2010

A common treatment in manufacturing web‐like thin materials like paper is to manipulate it between two cylinders under rolling contact. A roll press is sensitive to vibration, which is unwanted, because it marks the web by regular stripes. A piezoelectric actuator is an excellent device for vibration control applications because of its large force generation, very short response time and easy controllability. Control of piezoelectric actuator is straightforward by direct compensation of input voltage. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Nonlinear Vibration Behavior of Elastohydrodynamic Contacts
Authors: Wiegert Benedikt , Deppler Jens , Hetzler Hartmut , Seemann Wolfgang
Published: November 2010

The nonlinear dynamic behavior of a simple system with an elastohydrodynamic line contact is investigated. The elastohydrodynamic problem is solved with finite differences including streamline upwind techniques. The results are stored in a lookup table for an effective calculation of the frequency response. It is found that the system exhibits rich nonlinear dynamic behavior including jump phenomena as well as sub‐ and superharmonic bifurcations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Untersuchung irreversiblen Materialverhaltens mithilfe eines auf thermodynamischen Prinzipien basierenden Ansatzes
Authors: Müller Wolfgang H. , Abali B. Emek
Published: November 2010

Bekanntlich verwendet man in der Materialwissenschaft „Prinzipe“, um die mögliche Form von Materialgleichungen einzuschränken. Insbesondere sind hier das Entropieprinzip (etwa in der Version der Thermodynamik irreversibler Prozesse (TIP) nach [1], der Clausius‐Duhem Formalismus nach [2] oder die Methode der Lagrange‐Multiplikatoren [3]) zu nennen. Darüber hinaus existieren Extremalprinzipe, also „Derivate“ des Entropieprinzips, etwa das Prinzip der minimalen Energiedissipation nach [4] oder das Prinzip der maximalen Entropieproduktionsrate (bzw. Dissipationsrate) nach [5]. Langfristig gesehen ist es unser Ziel, die Zusammenhänge zwischen diesen auf den ersten Blick unabhängigen Postulaten aufzuzeigen. Kurzfristig geht es in diesem Artikel darum, ein konkretes Randwertproblem zu studieren, an dem sich erstens die Entropieproduktionsrate explizit berechnen und ihre Maximaleigenschaften diskutieren lassen und zweitens der Übergang zwischen nichtlinear‐reibungsbehafteter Flüssigkeit zum starr‐plastischen, linear verfestigenden Festkörper vornehmen lässt. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental Investigation, Viscoelastic‐Plastic Modelling and Parameter Identification for Different Batches of 51CrV4 Steel
Authors: Al‐Baldawi Ammar , Schreiber Lothar , Wünsch Olaf
Published: November 2010

In this paper, differences of the mechanical behaviour of several batches of 51CrV4 are shown in elongational controlled tests. The consequences of modelling the behaviour are treated with a viscoelastic‐plastic model. For each batch, a new parameter set was obtained using an evolution based optimization strategy. Here, the average parameter set is shown to be inaccurate in case of using it for all batches. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Hybrid Micro­Macro­Model for the Description of Evolving Anisotropy in Finite Polycrystal Plasticity
Authors: Frankenreiter Ilona , Rosato Daniele , Miehe Christian
Published: November 2010

The paper outlines recent developments of an efficient computational micro‐macro modeling of evolving anisotropies in metallic polycrystals. Main focus is put onto large strain deformation processes where the anisotropy is caused by developments of crystallographic texture. We construct a hybrid micro‐macro framework that mixes ingredients of a purely macroscopic modeling with scale bridging operations of selected micromechanisms. On the micromechanical side, we develop a new algorithmic procedure to capture the crystal reorientation for evolving fcc and bcc textures based on a parametrization of rotations in the Rodigues space. The computational model provides a fast and robust method for the estimation of evolving textures. This computational tool for texture estimation is incorporated in a modular format into a micro‐macro‐model, where it governs the evolution of macrostructural tensors due to texture development. The general framework for the hybrid embedding is a purely phenomenological setting of anisotropic finite plasticity in the logarithmic strain space. The model provides an efficient and computationally handable two‐scale approach for the prediction of effects caused by complex microstructural changes in polycrystals. The capability of the proposed method is demonstrated by means of representative numerical examples. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromechanical modeling of talc particle reinforced thermoplastic polymers
Authors: Hempel Philipp , Hillenberg Alexander , Seelig Thomas
Published: November 2010

The present work aims at investigating the mechanical behavior of talc particle reinforced thermoplastic polymers. Therefore, micromechanical analyses are performed utilizing detailed finite element models of the explicitely resolved microstructure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling Metals At Finite Deformation
Authors: Lehmann Eva , Loehnert Stefan , Wriggers Peter
Published: November 2010

During metal forming processes, substantial microstructural changes occur in the material due to large plastic deformations leading to different mechanical properties. It is of great interest to predict the behaviour of these materials at different fabriction stages and of the final product.

At first glance, the behaviour of metals can be approached by an elastoplastic isotropic material model with a volumetric‐deviatoric split and isotropic hardening. In order to perform the calculations, a logarithmic strain is considered in the principal directions of stress and strain space, allowing to make predictions even at finite deformations.

Because of the actual nature of metals, the crystalline structure, the deformation at the microstructural level is much more complex. Due to the mathematically algorithmic form of an elastic predictor and a plastic corrector, the elastoplastic model can be extended to crystal plasticity which is similarly handled in terms of a critical resolved shear stress on defined slip planes in the crystal. Hardening can be modelled through a viscoplastic power law. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the variationally consistent modeling of material failure
Authors: Mosler Jörn
Published: November 2010

Material failure associated with cracks or shear bands is frequently analyzed by utilizing so‐called cohesive models. Such models are based on traction‐separation laws. Within such approaches, the stress vector of the considered crack or shear band is related to its conjugate variable being the respective displacement jump (such as the material separation or the crack opening). In the present work, a framework suitable for the analysis of shear bands is discussed. All models belonging to that framework are consistently derived from thermodynamical principles. Hence, the second law of thermodynamics is automatically fulfilled. Furthermore, a variational principle strongly relying on the postulate of maximum dissipation is elaborated leading finally to a variationally consistent implementation. More precisely, all state variables, together with the unknown deformation mapping, follow naturally from minimizing an incrementally defined potential within the presented algorithmic formulation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A fully covariant four‐dimensional formulation in material space‐time
Authors: Schnepp Johannes
Published: November 2010

A fully covariant formulation for a hyperelastic solid as a four‐dimensional space‐time manifold is presented. It admits arbitrary coordinate transformations mixing space and time. The geometrical structure of the manifold is represented by a tetrad field. A variational formulation is given which uses the tetrad field as extra dependent variables. This formulation is able to describe a homogeneous stress state in a defect‐free crystal lattice. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Quantification of the evolution of shape storage and recovery in thermally responsive shape memory polymers
Authors: Steeb Holger , Kazakevičiūtė‐Makovska Rasa
Published: November 2010

This study demonstrates the relevance of strain and stress storage/recovery profiles for the thermomechanical behaviour of thermally responsive Shape Memory Polymers (SMPs). It is shown how these experimentally determined profiles may be used for the development, calibration and validation of continuum‐based models describing the shape memory effect in polymeric materials. The presented methodology applies both to small and finite strain deformation problems under the assumption of constant strain and cooling/heating rates. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Two‐mechanism models ­ some aspects of modelling
Authors: Wolff Michael , Böhm Michael , Suhr Bettina
Published: November 2010

Two‐mechanism (or, generally, multi‐mechanism) models have been studied for the last twenty years. Besides one‐mechanism (or “Chaboche”) models, they are a useful tool for modelling inelastic behavior. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling internal erosion of cohesionless soils using a microstructural parameter
Authors: Becker Christian , Kurzeja Patrick , Steeb Holger
Published: November 2010

Internal erosion processes are of vital importance for the risk management of geotechnical structures as well as for the understanding of the macroscopic mechanical and hydraulic properties of the subsoil in various man‐made constructions. Here, a 4‐phase continuum model is presented and numerically applied to illustrative applications. The role of interfacial area and related microstructural parameters is addressed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Modeling of Finite Nonlinear Visco­Electroelasticity
Authors: Büschel Alexander , Klinkel Sven , Wagner Werner
Published: November 2010

Polymeric electroelastic materials, so called electroactive Polymers (EAP) own the characteristic to deform by the application of an electrical field. Dielectric Elastomer (DE) actuators, belong to the group of electroactive Polymers. This type of actuator consists of soft elastomer between compliant and conducting electrodes. For the elastomer often silicones and acrylic elastomers are used. This material show in general a visco‐hyperelastic behavior. Therefore, models which describe large strains and viscoelasticity are required for the calculation of such actuators. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fully Coupled Thermo‐Hydrodynamic Simulation Model for Journal Bearings
Authors: Esmaeili L. , Schweizer B.
Published: November 2010

The isothermal form of Reynolds fluid film equation is used to predict the pressure generation in hydrodynamic journal bearings if temperature effects are neglected. Often, however, temperature effects may be important and cannot be neglected, because oil viscosity significantly varies with temperature. Also, thermal expansion of journal shaft and bearing housing must be taken into account since the bearing clearance changes with increasing temperature. Hence, the Reynolds pressure field equation, the energy equation for the fluid film and the heat transfer equations for journal and bearing housing have to be solved simultaneously. The coupled thermo‐hydrodynamic fluid flow problem is mathematically defined by a system of nonlinear integro‐differential equations. The governing equations are discretized and solved by a finite element approach. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A tetragonal switching model for ferroelectric materials
Authors: Keip Marc‐André , Schröder Jörg
Published: November 2010

In this work a tetragonal material model for ferroelectric materials including a microscopically motivated switching criterion is presented. The resulting formulation is able to describe ferroelectric switching effects on a microscopic scale under consideration of the natural tetragonal structure of the ferroelectric material. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adjoint Sensitivity Analysis of a Fluid‐Structure Interaction Problem
Authors: Marius Stoia‐Djeska , Carmen Anca Safta , Florin Frunzulica
Published: November 2010

A fluid‐structure mathematical model usually includes parameters whose actual values are known only approximately or can vary around some reference values. The objective of the sensitivity analysis is to determine quantitatively the behavior of the responses of a fluid‐structure system locally around a chosen point of the trajectory in the phase‐space of parameters and dependent variables. In this work, the response considered is the total mechanical energy of the structure. The sensitivities with respect to all the parameters the fluid‐structure system depends on are useful in many situations as well as for optimization purposes. We present the theoretical developments necessary for the application of the adjoint sensitivity analysis methods (ASAM) for the fully coupled governing equations of an aeroelastic system. The algorithm is general and can be applied for any kind of fluid‐structure interaction problems. Illustrative numerical examples are presented for the case of typical section with two degrees of freedom. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite element methods for strongly‐coupled systems of fluid‐structure interaction with application to granular flow in silos
Authors: Reinstädler Sven , Zilian Andreas , Dinkler Dieter
Published: November 2010

A monolithic approach to fluid‐structure interactions based on the space‐time finite element method is presented to investigate stress states in silos filled with granular material during discharge. The thin‐walled silo‐shell is discretized by continuum based, mixed‐hybrid finite elements, whereas the flowing granular material is described by an enhanced viscoplastic non‐Newtonian fluid model. To adapt the mesh nodes of the fluid domain to the structural deformations, a mesh‐moving scheme using a pseudo‐solid is applied. The level‐set‐method involving XFEM is used, including a 4D split algorithm for the space‐time finite elements, in order to describe free surfaces. The method is applied to 3D silo discharges. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite deformations of thin shells with piezoelectric sensors and actuators
Authors: Vetyukov Yury
Published: November 2010

We treat coupled electromechanical problem of finite deformations of piezoelectric shells with the help of the direct approach. A shell is considered as a material surface with mechanical degrees of freedom of particles and with an additional field variable, namely electric potential on the electrodes. This results both in the nonlinear system of equations of piezoelectric shells and in the appropriate numerical scheme. Application of the direct approach is preceded with the three‐dimensional asymptotic analysis of a linear electromechanical problem for a non‐homogeneous piezoelectric plate, which provides the constitutive relations for the nonlinear theory. As a sample problem, we present finite element analysis of deformation and local buckling of cylindrical panel, equipped with piezoelectric sensors. The latter influence the mechanical behavior and produce signals, which can be interpreted in terms of structural entities. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of a Viscoelastic Material Model in Electro‐Mechanics
Authors: Vogel Franziska , Steinmann Paul , Göktepe Serdar , Kuhl Ellen
Published: November 2010

In this contribution, the numerical modeling of electro‐viscoelastic material is considered. The electro‐mechanical problem formulated in terms of a symmetrized stress tensor is extended to a viscoelastic material model. For the incorporation of the viscosity model, the logarithmic strain space setting is utilized which mimics the small strain setting. Therefore a rheological model for viscosity from the geometrically linear theory can be used. Numerical examples for a typical uniaxial tensile test show the capability of the method to demonstrate typical relaxation and creep behavior. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Chemo‐Thermo‐Mechanics Coupling Applied in Hardened Cement Paste
Authors: Wu Tao , Wriggers Peter
Published: November 2010

In this contribution, the model of concrete deterioration due to alkali silica reaction(ASR) at the microscale is set up. Based on a three‐dimensional micro computer‐tomography, a finite‐element mesh is constructed at the micrometer length scale and 3D coupled Chemo‐Themo‐Mechanics model in hardened cement paste(HCP) accounting for diffusion, heat transport, micro‐crack is developed with staggering method. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Construction of Statistically Similar Representative Volume Elements Based on the Lineal‐Path Function
Authors: Brands Dominik , Balzani Daniel , Schröder Jörg
Published: November 2010

In this contribution we propose a method for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs and which represent quite accurately the mechanical response of the real material. For the design of such SSRVEs an objective function is minimized taking into account least‐square functionals based on suitable statistical measures, that characterize the inclusion morphology. Here, we find that the incorporation of the lineal‐path function leads to promising results in FE2‐simulations of macroscopically homogeneous boundary value problems as well as inhomogenous ones. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of Homogenization FEM Analysis to Aluminum Honeycomb Core Filled with Polymer Foams
Authors: Burlayenko Vyacheslav N. , Sadowski Tomasz
Published: November 2010

The effect of polyvinyl chloride (PVC) foam filler on elastic properties of a regular hexagonal aluminum honeycomb core is studied. The unit cell strain energy homogenization approach based on the finite element method (FEM) within ABAQUS code is applied for prediction of effective material constants of the foam‐filled honeycomb core. The developed FE model is then used to observe a three‐dimensional stress state over the hexagonal unit cell and, thereby, to assess the influence of the foam‐filling on the distribution of the local interfacial stresses. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Development of an elastic‐plastic constitutive model for highly anisotropic materials
Authors: Haasemann Georg , Lux Christian , Ulbricht Volker
Published: November 2010

Homogenization methods are used to obtain the effective properties of highly anisotropic materials such like textile reinforced composites. The state of the art is the utilization of this method to compute elastic properties. But the consideration of inelastic and anisotropic properties requires the application of more advanced techniques such as the FE2‐method. Due to the high numerical effort induced by this approach, this paper presents a new method to evaluate inelastic properties of an heterogeneous elastic‐plastic material. The parameters describing the inelastic properties require a modification of the return mapping algorithm which is used for the numerical implementation. Finally, the verification shows the accuracy of the results obtained with this new homogenization method. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A new and efficient approach for modeling short fiber reinforced materials within RVEs using an embedded element technique
Authors: Hoffmann S. , André M. , Rodríguez Sańchez A. , Mueller R.
Published: November 2010

This paper focuses on the numerical homogenization by using representative volume elements (RVE method). A new approach is presented that is capable of speeding up the modeling process and reducing the computation time of RVEs significantly. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Homogenization Approach Based on Laminates
Authors: Klusemann Benjamin , Svendsen Bob
Published: November 2010

In this work, a homogenization approach for the modeling of the material behavior of two‐phase composites motivated by modeling a thin‐layer‐type microstructure is presented. The basic idea here is to idealize the thin‐layered microstructure as a first‐order laminate. In particular, a jump in deformation state across the phase interface is modeled constitutively via a rank‐one connection of habit‐plane type. In the material framework, the value for the jump as well as its direction remain as independent constitutive variables. However, in the case of laminates and an ideal plain interface, the direction is given and stays in a first approach constant. We assume that their values are determined by mechanical and configurational equilibrium in the two‐phase composite at the interface. This yields to a set of implicit equations which lead to the corresponding response of the structure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effective viscous sintering parameters for heterogeneous plate‐like structures using numerical homogenisation
Authors: Schmidt Ingo
Published: November 2010

A model to describe the sintering of plate‐like structures and the numerical technique to obtain its ingredients from the analysis of a given heterogeneous structure are described. Finite membrane strains are accounted for and numerical creep tests are used to extract suitably defined macroscopic viscosities and generalised sintering stresses for plate‐like structures. An example is analysed and compared to a full 3D simulation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Applying Cauchy‐Born rule for converting atomistic model to continuum model
Authors: Shan Wenzhe , Nackenhorst Udo
Published: November 2010

The Cauchy‐Born rule has been applied in the Quasicontinuum method to derive continuum material properties based on underlying atomistic model in a physically consistent way. In this short work, the procedure is demonstrated, where the resulted materials constants are compared with experimental data found in literature. Moreover, the condition for applying the Cauchy‐Born rule is discussed, with an intuitive explanation for why it can be only applied to crystalline materials with perfect structure. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micromechanically based stress and strain‐rate flow potentials for anisotropic polycrystals
Authors: Tsotsova Rumena , Böhlke Thomas
Published: November 2010

The dissipation of rigid‐viscoplastic material behaviour is related to the stress flow potential and its Legendre‐Fenchel conjugated strain‐rate flow potential. In this paper micromechanically based approximation of these flow potentials, expressed in terms of the deviatoric stresses and strain‐rates, is derived from texture measurements. The dual potentials for single face‐centered cubic crystals are approximated in terms of Fourier expansion with tensorial texture coefficients. The macroscopic flow stress and strain‐rate potentials for an aggregate of polycrystals can be deduced from those of single crystal under the assumption of either homogeneous strain‐rate, or homogeneous stress field from the codf measurements. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Turbulent Poiseuille flow with near‐critical wall transpiration
Authors: Vigdorovich Igor , Oberlack Martin
Published: November 2010

An incompressible, pressure‐driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse velocity component, is considered. A closure condition is formulated, which relates the shear stress with the first and the second derivatives of the longitudinal mean velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary‐value problem for a second‐order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction velocity. The case of near‐critical transpiration, when the shear stress at the injection wall vanishes, is considered. It is shown that the maximum point on the mean velocity profile lies in a thin sublayer near the suction wall in this case. A formula for the position of the maximum point as a function of the transpiration factor is obtained. The mean velocity profiles near the suction wall are calculated. A friction law for Poiseuille flow with near‐critical transpiration is found, which makes it possible to describe the relation between the shear stress at the wall, the Reynolds number, and the transpiration velocity by a single function of one variable. Direct numerical simulation of the flow for some transpiration factors is performed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A hybrid model for electroosmotic flows in microchannels induced by internal electrodes
Authors: Stieglitz Ina , Ehrhard Peter
Published: November 2010

Internal electrodes, adjacent to insulating walls at defined zeta potential, lead to a non‐continuous potential distribution at the wall. Hence, simplified treatment appears problematic due to the singularity of the electrical field strength. To avoid this difficulty, we develop a hybrid model, which solves the electrical problem, including a resolution of the EDL, while the flow problem is solved in the fluid bulk only. We apply this hybrid model to investigate the position of internal electrodes with regard to their influence onto the flow field, driven by electroosmosis in a modular rectangular microchannel. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Stokesian Dynamics Method and the Settling behaviour of Particle‐Fibre‐Mixtures
Authors: Feist Markus , Keller Florian , Dörfler Willy , Nirschl Hermann
Published: November 2010

Sedimentation of fibres and particles can be observed manifold in industrial application. In waste water treatment, the water is clarified from solid particles and fibres utilizing sedimentation. Some filtration processes use fibres as an aid to improve the filtration quality. Finally, in the paper recycling process, one tries to separate cellulose fibres from inorganic particles used as filling material or in printing colours. For all these applications, it is necessary to understand the hydrodynamic interactions between single particles as well as particle and fibre collectives.

In the present paper, the sedimentation behaviour of fibres and particles is considered in detail. Mathematic modelling is used to investigate inter particle influences in detail. In particular, a method called Stokesian Dynamics is used to simulate the settling of fibres and particles. The main challenge of the modelling is the dependence of the direction of each fibre on its sedimentation velocity and the different sizes of the particles in a poly‐modal particle size distribution. Additionally fibres, particles and the fluid are influencing each other in a significant manner and in a long range. Therefore, while calculating the force on a particle, one has to take into account the influences of many particles. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling and Numerical Simulation of Breaking Waves on Structures
Authors: Fuchs Vilmar , Wünsch Olaf
Published: November 2010

This work deals with the analytical and numerical simulation of the loads on cylindrical offshore structures due to breaking waves. We investigate breaking waves impact on a cylindrical structure on the surface of the water by using a multiphase flow model of immiscible fluids based on the Volume of Fluid (VOF) method. Different numerical schemes are applied to identify the sharp interface between water and gas. The results are compared as well with the already existing experimental, analytical and numerical studies by [1‐3]. The agreement shows that the analytical and numerical models are suited to describe the experimental results. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Weakly 3D Transonic Flows in Narrow Channels
Authors: Kornfeld M. , Kluwick A.
Published: November 2010

Steady transonic flows through channels so slender that the classical boundary layer approach fails are considered. The resulting viscous inviscid interaction problem for weakly three‐dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes two‐dimensional in the leading order approximation. The behavior of the flow upstream of a surface mounted three‐dimensional obstacle will be demonstrated. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Heat Transfer through the Boundary Layer on a Moving Cylindrical Fibre
Authors: Redmond Brendan , McDonnell David
Published: November 2010

This paper applies boundary layer theory to the process of manufacturing polymer fibres known as the melt spinning process. The rate of heat loss of the fibre during this process, characterised by the local Nusselt number, is evaluated by means of a Pohlhausen integral method. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fluid‐Structure Interactions in ALE and Fully Eulerian Coordinates
Authors: Richter Thomas , Wick Thomas
Published: November 2010

We present a novel approach to treat fluid‐structure interactions in a closed variational setting. The standard model is the so‐called ‘arbitrary Lagrangian‐Eulerian’ (ALE) framework. Here, the fluid is transformed into an artificial coordinate system, which fits with the Lagrangian structure system. In the fully Eulerian framework, which is the reverse to ALE, the fluid is left in its natural coordinates while structure is transformed. With this approach, very large deformations, change of topology as well as free movement of the structure can be computed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crystallization waves in thin amorphous layers on heat conducting substrates
Authors: Buchner Christoph , Schneider Wilhelm
Published: November 2010

A crystallization process in thin films is considered, where, driven by the release of the latent heat of fusion, the transformation from an amorphous state to the crystalline state takes place in a progressing wave of invariant shape. The crystallization rate is determined by a rate equation. The influence of the heat loss due to heat conduction into the substrate is taken into account. The resulting system of an ordinary differential equation and an integro‐differential equation is solved numerically using a collocation method. The propagation speed of the wave in dependence on a non‐dimensional heat loss parameter is determined. It turns out that the existence of a self‐sustaining crystallization wave requires the heat loss parameter to be smaller than a certain critical value. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of Sound Radiated by Axisymmetric Vortex Ring
Authors: Alexandru Dumitrache , Horia Dumitrescu , Florin Frunzulica
Published: November 2010

A theoretical and numerical study using the unsteady, 3D Navier‐Stokes equations to generate axisymmetric vortex rings is reported. Increasing the vorticity, the vortex ring transition to a turbulent state are analyzed. After transition to a turbulent stage, the self‐similarity of the temporal evolution of the flow is observed. Then we can compare sound radiated by the vortex ring to jet noise, at similar Reynolds number and low Mach number. The agreement between the simulation results and the simplified model is good. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dynamic Wave Propagation in Porous Media Semi‐Infinite Domains
Authors: Heider Yousef , Markert Bernd , Ehlers Wolfgang
Published: November 2010

The problem of dynamic wave propagation in semi‐infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half‐space and soil‐structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary‐value problems (IBVP).

Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid‐fluid aggregates. Based on the continuum‐mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi‐static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time‐integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two‐dimensional IBVP. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Receptor clustering on cell membranes
Authors: Daub Markus
Published: November 2010

Apoptosis is an important physiological process since it enables organisms to remove unwanted or damaged cells. The stimulus of the extrinsic signalling pathway of apoptosis is the clustering of TNF‐receptors on the cell membrane. We introduce a mathematical model for the clustering of TNF‐receptors on the cell membrane. Numerical simulations yield a time evolution of the receptor clusters. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the viscoelastodynamic problem with Signorini boundary conditions
Authors: Petrov Adrien , Schatzman Michelle
Published: November 2010

This note focuses on a viscoelastodynamic problem being subject to unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, the problem can be reduced to the pseudo‐differential linear complementarity problem through Fourier analysis. We prove that this problem possesses a solution, which is obtained as the limit of a sequence of solutions of penalized problems and we establish that the energy losses are purely viscous. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Γ‐convergence for one‐dimensional Ginzburg‐Landau functional with generalized Lipschitz penalizing term
Authors: Raguž Andrija
Published: November 2010

We use the approach developed in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761‐825 (2001) to obtain Γ‐convergence for a class of Ginzburg‐Landau functionals Iε(v), where v = v(s) is appropriate Sobolev function. We generalize results from the paper A. Raguž: Relaxation of Ginzburg‐Landau functional with 1‐Lipschitz penalizing term in one dimension by Young measures on micropatterns, Asymptotic Anal. 41(3,4), 331‐361 (2005), where original functional was penalized by 1‐Lipschitz function g = g(s). In this note we prove Γ‐convergence when g = g(s, v(s), v′(s)) under suitable growth conditions imposed on g. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of Nonlinear Stochastic Ship Dynamics Under Extended Wave Modeling
Authors: Dostal Leo , Kreuzer Edwin
Published: November 2010

Analytical criteria for risk assessment of ships in random seas are important for the development of new intact stability criteria and also for the first design stage, where many ship designs have to be compared. The analysis is performed by Stochastic Averaging. The results are compared to those obtained by Monte Carlo simulations. We use extended wave modeling by means of two independent stochastic processes realizing a traveling wave with random phase and amplitude corresponding to a prescribed sea spectral density. The righting lever curve in waves is approximated by a polynomial, while quasistatic equilibrium of the analyzed ship in waves is assumed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Approximate Gauss‐Newton Method for Robust Parameter Estimation
Authors: Binder Tanja , Kostina Ekaterina
Published: November 2010

We consider robust parameter estimation problems in which either the l1 norm or the Huber function of a measurement error vector used as cost functionals. In order to avoid high computational effort of computing exact derivatives needed for the solution of these problems with the Gauss‐Newton method, we suggest to use approximations of the derivatives in the occurring linearized subproblems. We show how the error introduced by using only approximated derivatives can be compensated by adding a correction term to the objective function of the linearized problems. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model reduction in topology optimisation analysing the inner structure of sensitivity matrices
Authors: Gerzen Nikolai , Barthold Franz‐Joseph
Published: November 2010

Topology optimisation models usually contain a great number of design variables and correspondingly lead to large matrices (pseudo load matrixandsensitivity matrix) which appear in sensitivity analysis. We applysingular value decomposition(SVD) to these matrices to analyse their inner structure. Based on the obtained information, we perform model reduction by transformation of the design variables into a lower‐dimensional space. Numerical examples illustrate the advocated theoretical concept. Reasonable results are obtained, based on only a fraction of all design variables. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)