bluuebunny/crossref_metadata_2025 huggingface dataset:
A Thermodynamically­Consistent Phase Field Model for Electromechanical Diffusive Crack Propagation
Authors: Hofacker Martina , Miehe Christian , Welschinger Fabian
Published: November 2010

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and for crack initiation in bodies free of defects. This drawback can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. In [1,2], we developed a phase‐field‐model of brittle fracture, which is conceptually in line with gradient‐type continuum damage models. Its global response is governed by an incremental variational principle, whose Euler equations describe the balance of linear momentum and the evolution of the crack topology. In this paper, the proposed model is extended to a thermodynamically consistent four‐field setting of coupled electromechanical fracture, based on a degrading mixed energy‐enthalpy functional and an over‐force‐type dissipation functional. These functionals are expressed in terms of the displacement, the electric potential, the fracture phase and its dual driving‐force fields. Evaluation of the necessary condition yields, in addition to the above mentioned Euler equations, the Gauss‐law of electrostatics. The capability of the proposed framewok for the description of electromechanically coupled crack propagation is demonstrated by means of a representative numerical example. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Damage and Failure of Metal/Fibre‐Reinforced Polymer Tensile Specimens with Inelastic Interface
Authors: Konchakova Natalia , Mueller Ralf , Barth Franz‐Josef
Published: November 2010

Hybrid specimens of metal and fibre‐reinforced polymer are applied in automotive and aerospace industry. The simulation and analysis of damage of such engineering structures is the focus of this research. The investigation includes a computation of the extension of single lap tensile specimen, produced by ultrasonic metal welding. The specimen is manufactured from CF‐PA66 ‐ fibre‐reinforced polymer and AlMg3 (AA5754), which is used as a metallic joining partner. The aluminium substrate is treated as an elastoplastic material. The polymer composite generally shows an orthotropic elastic behaviour. The interface material has been numerically modeled as an elastoplastic material with linear hardening, coupled with Lemaitre‐type damage. The finite element method is used for the investigation of so‐called interface elements. The geometry of the interface is a consequence of the welding sonotrode geometry. The behaviour of specimens with square and ring interface geometry are analysed. The influence of the interface geometry on the mechanical properties of the joint is shown. The increase of the damage parameter and the development of failure are described for both cases. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Implementation of a cohesive zone model for the investigation of the dynamic behavior of a rotating shaft with a transverse crack
Authors: Liong Rugerri Toni , Proppe Carsten
Published: November 2010

The influence of a transverse crack on the vibration of a rotating shaft has been at the focus of attention of many researchers. The knowledge of the dynamic behavior of cracked shaft has helped in predicting the presence of a crack in a rotor. Here, the changing stiffness of the cracked shaft is investigated based on a cohesive zone model. This model is developed for mode‐I plane strain and accounts for triaxiality of the stress state explicitly by using basic elastic‐plastic constitutive relations. Then, the proposed numerical solution is compared to the switching crack model, which is based on linear elastic fracture mechanics. The cohesive zone model is implemented in finite element techniques to predict and to analyse the dynamic behavior of cracked rotor system. Timoshenko beam theory is used to model the discrete shaft under the effect of gravity, unbalance force and gyroscopic effect. The analysis includes the cohesive function for describing the breathing crack and the reduction of the second moment of area of the element at the location of the crack. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of material failure by combining the advantages of embedded strong discontinuity approaches and classical interface elements
Authors: Radulovic Radan , Mosler Jörn
Published: November 2010

A finite element formulation within the framework of the Strong Discontinuity Approach suitable for the simulation of crack growth is presented. The formulation allows for intersecting discontinuities and similarly to classical interface elements, the cracks are introduced parallel to the element facets. However and in contrast to interface elements, the discontinuities are directly embedded in finite elements, based on the Enhanced Assumed Strain concept. It is shown that a realistic prediction of the mechanical response requires the consideration of more than one crack within each finite element. The proposed formulation is suitable to overcome locking effects and it automatically fulfills crack path continuity. The approach is strictly local yielding an efficient numerical formulation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the search of supersingularities, more severe than a common crack singularity
Authors: Sator Christian , Becker Wilfried
Published: November 2010

Stress singularities at two‐dimensional multi‐material‐junctions, consisting of dissimilar, homogeneous, isotropic and linear‐elastic wedges under a plane strain state are considered. The stresses formed at the vertex of this multi‐material composite situation are analyzed by complex variable method, based on a choice of the Kolosov‐potentials which are applicable in the vicinity of the vertex. The characteristic equation for the order of the stress singularities is available in a closed‐form analytical manner and investigated numerically. By varying parameters, like the stiffness ratio of one material with respect to the remaining stiffnesses or the angle between the involved sectors of the junction, useful information about the variation of the order of the stress singularities is provided. A particular outcome of the performed investigations is that there are many situations where supersingularities occur, i.e. singularities more severe than those due to a crack inside a homogeneous material. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of the Arlequin method in the virtual engineering design process
Authors: Barthel Corinna , Gabbert Ulrich
Published: November 2010

The creation of a holistic model which is able to represent the global dynamic behavior as well as local effects in certain regions leads to finite element models consisting of domains with different local meshes and a combination of different model dimensions. The different model domains have to be coupled such causing in an additional coupling error. The Arlequin method seems to be a flexible tool which has some advantages in comparison to alternative methods. In this paper the application of the Arlequin method on the coupling of a 3D continua model and a beam model is studied. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the theory of orthotropic porous elastic rods
Authors: Bîrsan Mircea , Altenbach Holm
Published: November 2010

We employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. In this purpose, we consider the direct approach to the theory of rods, in which the thin body is modeled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. For orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three‐dimensional elasticity constants by solving several problems in the two different approaches (directed curves and three‐dimensional rods). (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Static and dynamic analysis of cracked or weakened structures
Authors: Carl Oliver , Zhang Chuanzeng
Published: November 2010

Stiffness modifications in engineering structures, for example due to damage and cracking, will inevitably also lead to changes in deformations, internal forces, natural frequencies and mode shapes of the structures. In this paper, an efficient and simple method for sensitivity analysis of cracked or weakened structures under time‐harmonic loading is presented. The method is based on a comparison between the strain energy and the kinetic energy of an uncracked structure and that of a cracked structure in conjunction with the application of exact or approximate Green's functions as described in [3] for the static case. The present analysis enables the prediction of any changes in the displacements and stresses and has a lower computational effort as compared to available classical methods, because only the damaged region has to be re‐considered in the method. Green's functions are taken as a basis of the approach, which have the ability to weight the influence of the stiffness modifications in a region of a structure and show how sensitive other regions respond to the stiffness modifications.

Based on linear elastic fracture mechanics, cracked or damaged regions are approximated by spring models in the analytical solution of some simple beam problems, while cracked finite elements are used for complicated cases where analytical solutions cannot be obtained. Sensitivity analysis with Green's functions (SAGF) approach is applied to static and dynamic analysis of cracked and weakened structures, which consist of homogeneous materials or fiber reinforced composites like reinforced concretes. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structure preserving integrators for non‐linear structural dynamics
Authors: Franke Marlon , Betsch Peter , Hesch Christian
Published: November 2010

A well known and major drawback of standard time integration schemes in the field of non‐linear elastodynamics is their unstable behavior in the case of stiff material behaviour. Even second order accurate implicit time integration schemes are unable to resolve the problem under consideration effectively. To remedy this drawback, structure preserving integrators have been developed. Therefore, the goal of this paper is to compare recently developed integrators. In particular, an energy and momentum conserving scheme, based on a publication by Betsch & Steinmann [1], as well as a symplectic variational integrator, proposed by Lew et al. [4] and Wendlandt & Marsden [3], based on a mid‐point evaluation of the discrete Lagrangian, are presented. Two representative numerical examples will outline the characteristics of the different approaches. In particular, a stiff non‐linear spring pendulum and a finite element model of non‐linear structural dynamics are considered. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Prediction of Time‐Dependent Structural Responses with Recurrent Neural Networks
Authors: Freitag Steffen , Graf Wolfgang , Kaliske Michael
Published: November 2010

A concept for the mapping of fuzzy structural action processes onto fuzzy structural response processes is presented. Recurrent neural networks for fuzzy data are developed for this mapping. The presented method can be applied to the model‐free numerical prediction of time‐dependent structural responses. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Verified Monotonicity‐Based Solution of a Simple Finite Element Model with Uncertain Node Locations
Authors: Smith Andrew P. , Garloff Jürgen , Werkle Horst
Published: November 2010

A tight verified solution enclosure is obtained for the node displacements of a simple truss model, whose parameters, including the node locations, are uncertain. The solution is based on a monotonicity analysis of these interval parameters. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Inverse Form Finding For Anisotropic Materials
Authors: Germain Sandrine , Scherer Michael , Steinmann Paul
Published: November 2010

The main goal of this paper is to extend the work of Govindjee and Mihalic (1996) to anisotropic hyperelasticity that is formulated in the logarithmic strain space involving a spectral decomposition of the right Cauchy‐Green tensor. Beside the theoretical aspects, we present a numerical example. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mortar‐Based Contact Formulation for Large Deformations
Authors: Hammer Michael E.
Published: November 2010

The discontinuities due to the discretization lead to some challenges. First, the normal direction of the contact surface is not steady because the discrete surface is only C0 continuous. One might smooth the normal vector field. Second, the question of contact enforcement has to be cleared. Contact forces can be modeled with either a Lagrange multiplier method or a penalty formulation to prevent penetration. Third, there must be developed a integration scheme which is able to handle the non‐steady boundary. Last, there is a strong discontinuity in measuring the penetration, where different criteria for enabling or disabling contact can be found (active set strategy). In this work, different approaches to solve this tasks are presented and brought into context. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Load and frequency interaction in dynamic buckling of soft‐core sandwich plates and shells
Authors: Hohe Jörg
Published: November 2010

The present study is concerned with an analysis of load‐frequency interaction effects in the dynamic buckling response of soft‐core sandwich plates and shells. Based on a higher‐order geometrically non‐linear sandwich shell theory in conjunction with an extended Galerkin procedure, a mathematical model together with analytical solution for simply supported sandwich plates and shells with with rectangular projection is obtained. By linearization of the non‐linear solution with respect to the oscillating parts, the interaction of the natural frequencies with static preloads can be analyzed. The results reveal that the transverse compressibility of soft sandwich cores might have distinct effects on the natural frequencies. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Buckling Analysis of Carbon Nanotubes
Authors: Hollerer Stefan
Published: November 2010

In this work, an atomistic‐continuum model is applied to single‐walled carbon nanotubes. The constitutive behaviour is described by the interatomic Tersoff‐Brenner potential. The coupling between atomistic deformation and the deformation of the continuum is done by an expanded Cauchy‐Born rule. With the help of this model, the buckling behaviour of carbon nanotubes under different loading conditions is studied. Numerical simulation results are given for two different types of loading (axial compression, torsion). (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Implementation of the Nitsche approach for various contact kinematics
Authors: Izi Ridvan , Konyukhov Alexander , Schweizerhof Karl
Published: November 2010

Numerical approaches are in case of contact problems mainly dealing with additional terms enforcing constraints. Within the Nitsche approach the inclusion of constraints for the non‐penetration and equilibrium of stresses of the contacting bodies is carried out in a fully variational sense. Taking into account a specific choice and the physical meaning of the encountered Lagrange multipliers two different schemes for the Nitsche formulation are obtained. Both types of the Nitsche approach are implemented in a nonlinear element and verification with numerical examples is done. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Vibrations of thin tolerance‐periodic plates
Authors: Wirowski Artur , Jędrysiak Jarosław , Kaźmierczak Magda
Published: November 2010

In this contribution, linear‐elastic thin plates with a tolerance‐periodic structure in planes parallel to the plate midplane are considered. It is assumed that their averaged (macroscopic) properties are described by continuous, slowly‐varying functions. Hence, plates of this kind can be treated as plates with a functionally graded structure. Here, free vibrations frequencies of a plate band are calculated within the proposed averaged model using the finite differences method. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Necessary and Sufficient Conditions for Zero‐stiffness Postbuckling
Authors: Jia Xin , Höfinger Gerhard , Mang Herbert A.
Published: November 2010

In the course of sensitivity analysis of the initial postbuckling behavior of elastic structures, a special case may occur which is referred to as zero‐stiffness postbuckling. The purpose of this paper is to present sufficient and necessary conditions for this special case which is associated with a favorable form of transition from imperfection sensitivity to imperfection insensitivity in the course of sensitivity analysis of the initial postbuckling path. Koiter's initial postbuckling analysis is chosen as the vehicle for quantification of the initial postbuckling behavior. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Contact simulation for the calculation of the kinematic excitation of vibrations from surface roughness of wheel and rail
Authors: Klotz Christian , Beitelschmidt Michael , Quarz Volker
Published: November 2010

A simulation method has been developed to predict the sound emission of the railway wheelsets due to the excitation of wheelset vibrations by surface roughness of wheel and rail. This model treats the contact in a linearized manner and is therefore not capable of modelling the local effects of the roughness in the wheel‐rail contact zone. These effects are very important since the contact acts as a low pass filter which is calculated within a contact simulation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Contact interaction inside knot connections of cables
Authors: Konyukhov Alexander , Schweizerhof Karl
Published: November 2010

Knots as a method for the fastening of ropes and other linear materials are widely appearing in practical applications ­ in sailing, in surgery, in textile and rope structures etc. The mechanics of knots, however, appears to be not sufficiently covered neither by analytical methods, nor by computational methods. From a computational mechanics point of view a knot is a perfect example requiring both a robust smooth cable element and a robust curve‐to‐curve contact algorithm. The current contribution is aimed on the development this combination ­ the isogeometric approach for curvilinear beams and the robust curve‐to‐curve contact algorithm for curvilinear cables. The developed model is applied studying the mechanics of various knots. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Higher‐Order Composite Beam Theory for Closed‐Form Analysis of Beams with Box and I Cross‐Section
Authors: Kroker Andreas M. , Becker Wilfried
Published: November 2010

For many cases of beam structures such as composite beams with box or I cross‐sections, shear forces can not be neglected and it is necessary to take shear deformation into account. Therefore, a higher‐order theory for composite beams is developed. The cross‐section of the beams can be divided into webs and flanges, both are assumed to have different symmetric layups with balanced angles. The axial displacement representation is chosen to be of second‐order for the flanges and of third‐order for the webs. There is no transverse contraction allowed. All parts of a cross‐section are assumed to have the same deflection in vertical direction. The geometric coupling of the flanges and webs is ensured by corresponding constraints. Based on the introduced kinematic representation, the principle of minimum potential energy is used to derive the respective differential equations. These governing equations are solved in a completely closed‐form analytical manner. This way, a closed‐form description of the whole beam behavior is achieved. In particular, all resultant local in‐plane stresses can be obtained directly. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Design of continuous strain‐type sensors for systems of structural mechanics
Authors: Krommer Michael , Vetyukov Yury , Zellhofer Markus
Published: November 2010

In this paper, we present a general approach for designing continuous strain‐type sensors to measure specific kinematical entities in systems of structural mechanics. We first discuss the case of three‐dimensional bodies in the geometrically linear regime, for which the solution of the sensor design problem is found from a problem‐oriented application of a work‐based integral formulation to an auxiliary problem of statics; yet, the resulting sensor works for static and dynamic problems. The deduction of solutions for the sensor design problem on a structural mechanics level is straightforward, because the three‐dimensional solution is work‐based. Hence, for any theory of structural mechanics, for which a corresponding work‐based integral formulation exists, we can easily find a solution of the sensor design problem. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Artificial neural network based inverse reliability analysis
Authors: Lehký David , Novák Drahomír
Published: November 2010

An inverse reliability analysis is the problem to find design parameters corresponding to specified reliability levels expressed by reliability index or by theoretical failure probability. Design parameters can be deterministic or they can be associated to random variables described by statistical moments. The aim is to solve generally not only the single design parameter case but also the multiple parameter problems with given multiple reliability constraints. A new general approach of inverse reliability analysis is proposed. The inverse analysis is based on the coupling of a stochastic simulation of Monte Carlo type and an artificial neural network. A novelty of the approach is the utilization of the efficient small‐sample simulation method Latin Hypercube Sampling used for the stochastic preparation of the training set. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Parametric vibration of TMD installed in tall building during seismic excitation
Authors: Majcher Krzysztof , Wójcicki Zbigniew
Published: November 2010

In this paper shaking‐table tests of a model‐scale building with TMD (tuned mass damper) are conducted. The main aim of the research is to show the influence of kinematical excitation on the dynamic response of the model of tall building with pendulum TMD. The special attention is focused on the functioning of pendulum, which is simultaneously excited by the vertical component of ground motion. There are two kinds of analysis carried out — numerical and experimental. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model‐scale building with TMD. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Highly Efficient Implementation of ANS/ EAS ‘Solid‐Shell’ Finite Elements for Explicit Time Integration
Authors: Mattern Steffen , Schweizerhof Karl
Published: November 2010

In an explicit time integration algorithm, the most time‐consuming part of an analysis is the computation of the internal nodal force vector. An implementation concept for element routines for volumetric shell ­ so‐called Solid‐Shell ‐ elements based on the application of the symbolic programming tool ACEGEN, a plug‐in for the computer algebra software MATHEMATICA is presented. Symbolic implementation means that vector and matrix operations and differentiations can be performed symbolically in order to generate program code, which supports the implementation, reduces programming effort and helps to avoid programming errors almost completely. The program code is generated in FORTRAN and simultaneously optimized automatically, which leads to very efficient routines compared to manually implemented code. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Eine analytische Lösung für die großen Deformationen bei den 4 Euler Knickfällen und ihre Anwendung auf Probleme der Mikroelektronik
Authors: Müller W. H. , Hauck T.
Published: November 2010

Die höhere IO‐Pin Anzahl bei geringer werdendem Abstand und bei gleichzeitiger Vergrösserung von Wafern erfordert neue Testverfahren zur elektrischen Funktionalität. Die sog. Vertical‐Buckling Probe‐Nadeltechnik scheint ein gutes Konzept bei der experimentellen Erfassung des Vorliegens elektrischen Kontaktes zu sein: Die bei der Kontaktierung mit dem Pad gegebene Elastizität der Nadel führt zum Eulerknicken dergestalt, dass ein mehr oder weniger konstanter Kontaktdruck während des relativ langen Wegvorschubes gegeben ist. Dadurch erzielt man bei der Produktionstestphase ein hohes Toleranzniveau, um den wechselnden Planaritätsbedingungen des Wafers zu begegnen. Zur Dimensionierung einer Buckling‐Needle‐Probe ist es günstig, über geschlossene Lösungen zu verfügen, welche die geometrisch nichtlineare Deformation in Verbindung mit einer über der ersten kritischen Knicklast liegenden Kraft setzen. Hierzu werden im Aufsatz analytische Lösungen der Differentialgleichung für die Elastica bei den Eulerfällen vorgestellt, diskutiert, angewendet und auch mit FE‐Berechnungen verglichen. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Poroelastodynamic Plate Formulation of Extendable Order
Authors: Nagler Loris , Schanz Martin
Published: November 2010

In order to model the sound insulation properties of porous plate‐like structures, an adequate poroelastic plate theory is needed. The approach used here to obtain such a theory consists in expanding the primal variables into power series in thickness direction. This allows an analytical integration over the thickness, thus reducing the dimension of the problem from 3d to 2d. The resulting out‐of‐plane and in‐plane problems are discussed. Numerical calculations show a good agreement between the proposed model and the three‐dimensional system. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Infinite elements in a poroelastodynamic FEM
Authors: Nenning Mathias , Schanz Martin
Published: November 2010

Wave propagation phenomena in unbounded domains occur in many engineering applications, e.g., soil structure interactions. When simulating unbounded domains, infinite elements are a possible choice to describe the far field behavior, whereas the near field is described through conventional finite elements. Finite element formulations for porous materials in terms of Biot's theory [1] have been published, e.g., by Zienkiewicz [2]. For infinite elements, several approaches are described in [3,4]. Infinite elements are based on special shape functions to approximate the semi‐infinite geometry as well as the Sommerfeld radiation condition, i.e., the waves decay with distance and are not reflected at infinity. If there is only one wave traveling in the media, a formulation in time‐domain can be established. But in poroelastodynamics, there are three body waves and eventually also a Rayleigh wave. Unfortunately, the extension to more than one wave is not straight forward. Here, an infinite element is presented which can handle all wave types, as it is needed in poroelasticity. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
High‐Order Time Integration in the p‐Version of Finite Elements
Authors: Netz Torben , Hartmann Stefan
Published: November 2010

In isothermal solid mechanics, the space and time domain need to be discretized. This paper presents an approach using high‐order finite elements based on Legendre polynomials for the spatial discretization and time‐adaptive diagonal‐implicit Runge‐Kutta methods for the temporal discretization. The superiority of this approach over a traditional one using linear shape functions for the space domain and a Backward‐Euler scheme for the time domain is demonstrated. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coupled FE‐Analysis Involving Partially Saturated Soils
Authors: Pertl Michael , Hofmann Matthias , Hofstetter Günter
Published: November 2010

A short introduction to the governing equations and the corresponding FE‐formulation of a three phase model for partially saturated soils is given and a constitutive law of the soil skeleton and its numerical integration is discussed briefly. Finally, the application of the numerical model is presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Heat conduction in transversally graded laminates with non‐uniform microstructure
Authors: Radzikowska Alina , Jędrysiak Jaroslaw
Published: November 2010

Two‐component laminates made of conductors distributed non‐periodically as laminas along one direction are considered in this note. The macroscopic properties of these laminates are described by continuous slowly‐varying functions across laminas. In order to analyse heat conduction, the approach, called the tolerance modelling, is used. The aim of this note is to use averaged equations of the tolerance model for transversally graded laminates to analyse stationary heat conduction across laminas. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computation of the Three‐Dimensional Stress State in Composite Shell Structures with Mixed Finite Elements
Authors: Schürg Marco , Wackerfuß Jens , Gruttmann Friedrich
Published: November 2010

Being able to compute the complete three‐dimensional stress state in layered composite shell structures is essential in order to examine complicated interlaminar failure modes such as delamination. We lay out a mixed finite element formulation with independent displacements, rotations, stress resultants and shell strains. A mixed hybrid shell element with 4 nodes and 5 or 6 nodal degrees of freedom is developed, so that the element formulation can also be used for problems with shell intersections. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Least‐Squares Mixed Finite Element for Quasi‐Incompressible Elastodynamics
Authors: Schwarz Alexander , Steeger Karl , Schröder Jörg
Published: November 2010

In the present work, a mixed finite element based on a modified least‐squares formulation is proposed. Here, we consider the time‐dependent equations for quasi‐incompressible elastodynamics under small strain assumptions. The main goal is to obtain an accurate approximation of both displacements and stresses in particular for the lowest‐order element. Basis for the element formulation is a weak form resulting from a least‐squares method. The L2‐norm minimization of the time‐discretized residuals of the given first‐order system leads to a functional depending on approximations for displacements and stresses. By introducing a time‐independent displacement test function, a weak form is derived. A numerical example concerning quasi‐incompressible elasticity shows the performance of the approach for the lowest‐order element RT0P1as. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Minimum Stiffness Criteria for Edge Reinforcements of Elastically Clamped Plates
Authors: Weißgraeber Philipp , Mittelstedt Christian , Becker Wilfried
Published: November 2010

In many structural situations, e.g. in aerospace engineering, composite plates with edge reinforcements are used, for example as stiffeners of a fuselage section of an airplane. Based on an explicit analysis of the buckling behavior of the laminate plate, a minimum stiffness criterion is presented in this contribution. A transformation of the governing equations into a dimensionless system is used, that proved to be very advantageous. Besides a minimum stiffness criterion that can be used for generation of minimum stiffness diagrams, an absolute minimum stiffness is found that enables the reinforcement to act like a simple support for arbitrarily slender plates. The relevance of the criteria for stiffener design is discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dynamical flexibility of damped vibratory clamped‐clamped beam in transportation
Authors: Żółkiewski Sławomir
Published: November 2010

This work concerns the issue of damped vibratory beam in transportation. Support conditions were defined for clamped‐clamped beamlike systems. Structural loads were defined as with unitary amplitude ones up to the used dynamical flexibility definition. Geometric representation of analyzed element is a beam with symmetric cross‐section constant on the whole length of the beam. The load assumed as bending one. The beam was fixed onto the rotational disk with the angular velocity treated as transportation velocity. In thesis the dynamical flexibility of analyzed beam was presented and the sample dynamical characteristics were drawn on graphical charts. In derived mathematical model mutual interactions between the damping forces, dynamical flexibilities and angular working velocity were took into consideration. Presented model can be put into use in high speed pumps and turbines as vanes. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability and Bifurcations of Rotors in Fluid Film Bearings
Authors: Boyaci Aydin , Seemann Wolfgang , Proppe Carsten
Published: November 2010

To study the nonlinear phenomena of rotors in the sense of bifurcation theory, the mechanical model of a symmetric flexible rotor is investigated which is supported by two identical journal bearings. Two types of journal bearings are considered. While the oil whirl and oil whip oscillations of rotors in plain journal bearings are widely examined, the floating ring bearings cause a quite different vibration behavior with several mode interactions and an area of so‐called critical limit cycles leading to a rotor damage. For both types a Hopf bifurcation marks the beginning of the self‐excited oscillations in the case of a perfectly balanced rotor. By applying the methods of numerical continuation the occurring limit cycles as well as their stability are determined. The different nonlinear effects with the corresponding bifurcations are explained by describing the global solution behavior of the rotor‐bearing systems. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Transverse Vibrations of a String Segment Between Two Supports Moving Axially Along a String of Infinite Length
Authors: Franze Andreas , Zastrau Bernd W.
Published: November 2010

This paper deals with the equation of motion of a string with time‐varying boundary conditions. This equation can be transformed to a partial differential equation (PDE) with non‐varying boundary conditions. During the solution process, the inverse of the time derivative operator is needed. To ensure the existence of a solution, the time derivative is generalized to a weighted time derivative on a weighted L2‐space. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bifurcation analysis of a stochastic non‐smooth friction model
Authors: Gaus Nicole , Proppe Carsten
Published: November 2010

Non‐smooth systems with stochastic parameters are important models e.g. for brake and cam follower systems. They show special bifurcation phenomena, such as grazing bifurcations. This contribution studies the influence of stochastic processes on bifurcations in non‐smooth systems. As an example, the classical mass on a belt system is considered, where stick‐slip vibrations occur. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, a stochastic process is introduced into the non‐smooth model and its influence on the bifurcation behavior is studied. It is shown that the stochastic process may alter the bifurcation behavior of the deterministic system. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Vibrational asperity interaction in slowly sliding contacts
Authors: Graf Matthias , Ostermeyer G.‐P.
Published: November 2010

When two elastic bodies slide against each other, contacting asperities carry tangential load. In the case of slow sliding, each asperity can show a stick‐slip‐like movement that can be modelled as an integrate‐and‐fire (IF) oscillator. Asperities influence each other by an elastic coupling which allows a globally synchronized state instead of local events. For two neighboured asperities, the dynamics of coupled IF oscillators is investigated in view of synchronization modes, energy dissipation and their significance for the tribological contact. Additionally, the influence of a relaxating coefficient of stiction, i.e. a time‐dependent firing threshold, is discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Untersuchung des Schwingungsverhaltens von Ölgemälden
Authors: Kracht Kerstin , von Wagner Utz
Published: November 2010

Gemälde der „Alten Meister“ sind unersetzbare Kulturgüter, die von hohem künstlerischen, kulturellen, ethisch‐religiösen, historischen, sozialen und/oder ökonomischen Wert sind. Daher hat der Schutz der Kunstwerke vor Beschädigungen höchste Priorität. Das große Interesse der Öffentlichkeit an Kulturgütern, wie den Ölgemälden, erfordert die Ausstellung der Gemälde und damit auch ihren Transport. Gemälde werden jedoch während der Exposition und des Transportes schädlichen, dynamischen Beanspruchungen ausgesetzt, was im Widerspruch zum Schutzbedarf steht. Da sich Ausstellungen und Transporte nicht vermeiden lassen, haben Restauratoren im Vorfeld die Aufgabe die Gemälde zu beurteilen, inwiefern diese den anstehenden Belastungen standhalten werden. Die Beurteilungskriterien sind subjektiver Natur und basieren auf sichtbaren Alterungsphänomenen.

Die vorliegende Veröffentlichung diskutiert die Ergebnisse experimenteller Schwingungsanalysen an speziellen Testobjekten, die nach „Art der Alten Meister“ hergestellt wurden. Grundlagen der Resultate sind Schwingungsantworten frischer und gealterter Ölgemälde, die mit Hilfe berührungsloser Lasertechnik gemessen wurden. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Solution of the Fokker‐Planck Equation with Time‐Discontinuous Galerkin Methods
Authors: Loerke Friederike , Nackenhorst Udo
Published: November 2010

The response of non‐linear dynamic systems under white noise excitation possesses Markov characteristics. The evolution of the probability density of the system response is represented by the Fokker‐Planck equation, which characterizes advection and diffusion. The solution probability density distribution often possesses high gradients. Therefore an efficient numerical solution technique based on a discontinuous Galerkin approximation in the time domain is proposed for the solution of the Fokker‐Planck equation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical and experimental investigations of dynamic contact phenomena in jointed structures
Authors: Süß Dominik , Geisler Johannes , Willner Kai
Published: November 2010

Structural dynamic properties like stiffness and damping are strongly influenced by contact phenomena in jointed structures. Therefore numerical and experimental investigations are presented, in order to understand and predict the behaviour of such mechanical devices. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the effect of different parameterizations of the flow rule on the efficiency of variational constitutive updates
Authors: Bleier Nikolaus , Bruhns Otto T. , Mosler Jörn
Published: November 2010

The numerical efficiency of so‐called variational constitutive updates for finite strain plasticity theory is analyzed. These updates compute the unknowns such as the plastic strains by minimizing an appropriate functional. Within the present paper, different parameterizations of the flow rule are utilized within the variational constitutive update scheme. It is shown that comparing to the return‐mapping algorithm, the variational updates require significantly less iteration steps and thus, is numerically highly efficient. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechanic‐Stochastic Model for the Simulation of Polycrystals
Authors: Montalvo‐Urquizo Jonathan , Bobrov Pavel , Schmidt Alfred , Wosnoik Werner
Published: November 2010

A mechanic‐stochastic model for the mechanics of polycrystal material based on the single crystal orientations is presented. With this method, the distributions of strain and stress tensor components can be obtained in practice. Specific examples of computed distributions are shown, together with the distributions of the FEM‐calculated mechanical responses of a polycrystal. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Estimate of the Thermoelastic Properties of Pyrolytic Carbon based on an Image Segmentation Technique
Authors: Böhlke T. , Lin S. , Piat R. , Heizmann M. , Tsukrov I.
Published: November 2010

The submicrostructure of Pyrolytic Carbon (PyC) can be described as an aggregate of approximately coherent domains with different orientations. The domains themselves exhibit a hexagonal material symmetry. In order to apply statistical homogenization schemes [1] which predict the thermomechanical properties in terms of the microstructural characteristics, a quantitative description of PyC microstructures based on experimental data is a precondition. In the study, a new efficient image segmentation technique is applied which extracts from micrographs the one‐ and two‐point correlation functions of domain orientation which are necessary for computing bounds of the thermo‐elastic properties of PyC. The segmentation technique, which segments the micrograph into regions with approximately coherent orientations, uses the distribution of Local Binary Patterns (LBPs) [4] for determining the similarity of adjacent image regions. This region‐based algorithm yields a first coarse image segmentation. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
3D finite element analysis of biofilm growth considering nutrient diffusion
Authors: Bolea Albero Antonio , Bertsch Christine , Böl Markus
Published: November 2010

There exist a lot of models that are able to describe the behavior of biofilm systems. They can be classified into (1) analytical models, (2) pseudo‐analytical models, and (3) numerical models. Based on the numerous advantages of numerical models in this work a 3D mechanical biofilm model is discussed and implemented into a finite element program in order to simulate growth effects coupled with the nutrient diffusion through the biofilm. Based on three‐dimensional biofilm structures, numerical examples are presented in order to show the ability of the new modeling approach. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiscale modeling of multiphase "in situ" composite
Authors: Bontcheva Nikolina , Parashkevova Ludmila
Published: November 2010

The elastic‐plastic behaviour of rapidly solidified Al based (FeSi)‐enriched alloys containing intermetallic compounds is considered. A new multilevel mechanical model for the “in situ” composite is proposed considering the aluminium matrix as a micropolar elastic plastic Cosserat material and the hardening phases as pure elastic ones. A two steps homogenization procedure is applied to obtain the overall properties of the multiphase “in situ“ composite, taking into account the existence of different sizes of intermetallic inclusions. A variational approach is applied to evaluate the equivalent stress on macro level at the transition from micro to macro scale. The model is developed using information provided by microstructural investigations and EDX analysis. The multistage bulk material manufacturing process from rapid solidified powders or ribbons is simulated using the Finite Element Method. The model is implemented as user subroutines into the FE code MARC. Numerical simulations are provided, corresponding to different values of metal forming parameters. The influence of the different inclusions sizes on the hardening behavior is discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermoviscoelasticity of fibre reinforced rubbery polymers
Authors: Dal Hüsnü , Kaliske Michael , Hickmann Rico , Cherif Chokri , Jurk Rene , Heinrich Gert
Published: November 2010

Fibre or textile reinforcement is commonly used in order to enhance the directional mechanical and thermal properties of rubbery polymers. For the quantitative analysis and design of fibre reinforced elastomeric materials, precise description of the composite behaviour plays a crucial role. To this end, a coupled thermomechanical formulation at finite strains is presented. The anisotropic thermal and mechanical properties are homogenized analytically throughout the constitutive description. For the description of the directional mechanical properties, logarithmic strain measures at fibre orientation direction are introduced in order to describe the fibre behaviour. The viscosity plays a crucial role in the heating of rubber components under cyclic loading. Contribution of thermodynamically consistent heat sources to the thermal problem are also considered. The coupled finite element implementation based on the isothermal split algorithm is demonstrated by a benchmark numerical example. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the thermo‐mechanically coupled simulation of poly‐crystalline Shape Memory Alloys
Authors: Junker Philipp , Hackl Klaus
Published: November 2010

We present a thermo‐mechanically coupled model for poly‐crystalline shape memory alloys which accounts both for the localized phase transformations and the resulting heat production. The model is based on the physical principles of energy conservation and entropy maximization. Choosing an appropriate ansatz for the entropy production the evolution equation for the phases can be derived as well the heat conduction equation. The results show good agreement to experimental findings. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiscale Modelling of the Effective Viscoplastic Material Behaviour of Textile‐Reinforced Polymers Using XFEM
Authors: Kästner Markus , Obst Martin , Brummund Jörg , Ulbricht Volker
Published: November 2010

In this contribution a modelling approach using numerical homogenisation techniques is applied to predict the effective nonlinear material behaviour of composites from simulations of a representative volume element (RVE). Numerical models of the heterogeneous material structure in the RVE are generated using the eXtended Finite Element Method (XFEM) which allows for a regular mesh. Suitable constitutive relations account for the material behaviour of the constituents. The influence of the nonlinear matrix material behaviour on the composite is studied in a physically nonlinear FE simulation of the local material behaviour in the RVE ­ effective stress‐strain curves are computed and compared to experimental observations. The approach is currently augmented by a damage model for the fibre bundle. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A micromechanically motivated model for ferroelectrics combined with polygonal finite elements
Authors: Kaliappan Jayabal , Menzel Andreas , Arunachalakasi Arockiarajan , M Srinivasan Sivakumar
Published: November 2010

Piezoelectric materials are one of the most prominent smart materials due to their strong electromechanical coupling behaviour. Ferroelectric ceramics behave like piezoelectric materials under low electrical and mechanical loads, but exhibit pronounced nonlinear response at higher loads due to microscopic domain switching. Modern smart devices consist of complex geometries that may force the ferroelectrics employed within them to experience higher fields than they were originally designed for, so that the material responds within its nonlinear region. Hence, models predicting the nonlinear effects of ferroelectrics under complex loading cases are important from the design point of view. Within standard finite element models dealing with electromechanical problems, each grain may be subdiscretized by several finite elements. This problem can be approximated or rather overcome by a polygonal finite element method, where each grain is modelled by solely one single finite element. In this contribution, a micromechanically motivated switching model for ferroelectric ceramics, as based on volume fraction concepts, is combined with polygonal finite element approach. Related representative numerical examples allow to further study and understand the nonlinear response of this material under complex loading cases. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)