Showing papers by "Peter Wriggers published in 2011"
TL;DR: In this article, a knot-to-surface (KTS) algorithm is developed to treat the contact constraints with NURBS contact surface discretizations, which is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over C 0 -continuous finite elements.
255 citations
TL;DR: In this article, a mortar-based approach is presented to treat the contact constraints, whereby the discretization of the continuum is performed with arbitrary order NURBS, as well as C0-continuous Lagrange polynomial elements for comparison purposes.
Abstract: This paper focuses on the application of NURBS-based isogeometric analysis to Coulomb frictional contact problems between deformable bodies, in the context of large deformations. A mortar-based approach is presented to treat the contact constraints, whereby the discretization of the continuum is performed with arbitrary order NURBS, as well as C0-continuous Lagrange polynomial elements for comparison purposes. The numerical examples show that the proposed contact formulation in conjunction with the NURBS discretization delivers accurate and robust predictions. Results of lower quality are obtained from the Lagrange discretization, as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface. Copyright © 2011 John Wiley & Sons, Ltd.
219 citations
TL;DR: In this paper, a homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media, based on appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation.
Abstract: A homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media. The approach is based on the appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation. Thermodynamical consistency that ensures standard thermoelasticity relationships among various macroscopic quantities is enforced through the explicit enforcement of the macroscopic temperature for all evaluations of temperature dependent microscale functionals. This enforcement induces a theoretical split of the accompanying micromechanical boundary value problem into two phases where a mechanical phase imposes the macroscopic deformation and temperature on a test sample while a subsequent purely thermal phase on the resulting deformed configuration imposes the macroscopic temperature gradient. In addition to consistently recovering standard scale transition criteria within this framework, a supplementary dissipation criterion is proposed based on alternative identifications for the macroscopic temperature gradient and heat flux. In order to complete the macroscale implementation of the overall homogenization methodology, methods of determining the constitutive tangents associated with the primary macroscopic variables are discussed. Aspects of the developed framework are demonstrated by numerical investigations on model microstructures.
94 citations
TL;DR: In this paper, the modified or corrected extended finite element method originally presented in Fries (Int. Numer. Meth. 2008; 75:503-532) for the 2D case is extended to 3D including different remedies for the problem that the crack front enrichment functions are linearly dependent in the blending elements.
Abstract: In this paper, the modified or corrected extended finite element method originally presented in Fries (Int. J. Numer. Meth. Engng. 2008; 75:503–532) for the 2D case is extended to 3D including different remedies for the problem that the crack front enrichment functions are linearly dependent in the blending elements. In the context of this extension, we address a number of computational issues of the 3D XFEM, in particular possible quadrature rules for elements with discontinuities. Also, the influence of finite deformation theory for crack simulations in comparison to linear elastic fracture mechanics is investigated. A number of numerical examples demonstrate the behavior of the presented possibilities. Copyright © 2010 John Wiley & Sons, Ltd.
84 citations
TL;DR: In this article, a mixed finite element with different interpolation orders of the terms related to the minors of the deformation gradient is developed, based on the knowledge that the minors play a major role for the transformation of infinitesimal line-, area and volume elements, as well as in the formulation of polyconvex strain energy functions.
64 citations
TL;DR: In this paper, a nonlocal cohesive zone model is derived taking into account the properties of finite thickness interfaces, and the functional expression of the stress separation relationship, which bridges the gap between continuum damage mechanics and nonlinear fracture mechanics, depends on the complex failure phenomena affecting the material microstructure of the interface region.
61 citations
TL;DR: In this article, a non-local cohesive zone model (CZM) is proposed for polycrystalline materials, focusing on the constitutive modelling of the finite thickness interfaces between the grains.
61 citations
TL;DR: Pimenta et al. as mentioned in this paper presented a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics, where the weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces.
Abstract: Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715---732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.
57 citations
TL;DR: In this article, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest, motivated by higher-order homogenization techniques.
53 citations
TL;DR: In this article, random homogenization analysis of heterogeneous materials is addressed in the context of elasticity, where the randomness and correlation of components' properties are fully considered and random effective properties together with their correlation for the two-phase heterogeneous material are then sought.
40 citations
01 Jan 2011
TL;DR: In this paper, a geometrically exact theory for contact interaction is proposed for entangled fibrous materials and a 3D contact smoothing method based on quasi-C1 interpolation is presented.
Abstract: From the content: Contact Modelling in Entangled Fibrous Materials.- 3D Contact Smoothing Method Based on Quasi-C1 Interpolation.- On a Geometrically Exact Theory for Contact Interactions.- Finite Deformation Contact Based on a 3D Dual Mortar and Semi-Smooth Newton Approach.- The Contact Patch Test for Linear Contact Pressure Distributions in 2D Frictionless Contact.
TL;DR: Among two optimal strategies proposed for optimization models, the second one can effectively reduce the workload by avoiding the computation of the variance of the dynamic response during the iterative process.
Abstract: In this work, a reliability-based optimization technique is addressed to obtain the minimum mean value of random mass of the structures with random parameters under stationary stochastic process excitation. The challenge of the problem lies in randomness involved from both structural parameters and dynamic load, which renders the structural reliability becoming the random dynamic reliability of the first passage problem. In order to obtain minimum mean value of random gross mass, element and system dynamic reliability constraints are constructed, respectively, and the structural sizing and shape optimization models based on the dynamic reliability are then presented. Moreover, among two optimal strategies proposed for optimization models, the second one can effectively reduce the workload by avoiding the computation of the variance of the dynamic response during the iterative process. Finally, the implementation of three examples is discussed to display the feasibility and validity of optimization technique given.
TL;DR: In this article, dimension and shape optimization of structures under stochastic process excitation is addressed in the context of element or system dynamic reliability constraints, where the structural gross mass is taken to be the objective function.
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08 Jul 2011
TL;DR: In this article, the authors model the internal friction of Silica Filled Elastomers on self-affine road surfaces and investigate the dynamic interaction between the wheel block and the road.
Abstract: Modelling of Dry andWet Friction of Silica Filled Elastomers on Self-Affine Road Surfaces.- Micromechanics of Internal Friction of Filler Reinforced Elastomers.- Multi-Scale Approach for Frictional Contact of Elastomers on Rough Rigid Surfaces.- Thermal Effects and Dissipation in a Model of Rubber Phenomenology.- Finite Element Techniques for Rolling RubberWheels.- Simulation and Experimental Investigations of the Dynamic Interaction between Tyre Tread Block and Road.- Micro Texture Characterization and Prognosis of the Maximum Traction between Grosch Wheel and Asphalt Surfaces underWet Conditions.
01 Jan 2011
TL;DR: In this paper, the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM) using a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles.
Abstract: Within this contribution the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM). The DEM uses a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles. To reduce computation times an efficient parallelization scheme is developed which is based on the Verlet list concept and the sorting of particles according to their spatial position. The macroscopic mechanical behavior of the particle model is analyzed through standard triaxial tests of periodic cubical samples. A technique to accurately apply stress boundary conditions is presented in detail. Finally, the triaxial tests are used to analyze the influence of the sample size and the particle shape on the resulting stress-strain behavior.
01 Jan 2011
TL;DR: The unified setting presented here is based on phase transformation (PTs) of monocrystalline shape memory alloys (SMAs) and includes polycrystalline SMAs whose microstructure is modeled using lattice variants of RVEs consisting of equal convex isotropically elastic grains with specific texture.
Abstract: The unified setting presented here is based on phase transformation (PTs) of monocrystalline shape memory alloys (SMAs) and includes polycrystalline SMAs whose microstructure is modeled using lattice variants of RVEs consisting of equal convex isotropically elastic grains with specific texture. A pre-averaging scheme for randomly distributed polycrystalline variants of PT strains is used transforming them into fictitious phase variants of a monocrystal. Thus, the integration process in parametric time and the spatial integration algorithms of the discretized variational problems for both mono and polycrystalline PTs are implemented into a unified algorithm with bifurcation within incremental time integration before spatial integration via finite element method. Furthermore, error-controlled adaptive 3D finite element method in space is presented for PT problems using an explicit a posteriori discretization error indicator with gradient smoothing and adaptive mesh refinements by new mesh generation in each adaptive step. Examples for full PT cycles and comparisons with experiment are presented.
TL;DR: In this paper, a finite crystal plasticity model is used to model the behavior of polycrystalline materials in representative volume elements (RVEs) of the microstructure, and a multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution.
Abstract: During sheet bulk metal forming processes both, flat geometries and three-dimensional structures change their shape significantly while undergoing large plastic deformations. As for forming processes, FE-simulations are often done before in situ experiments, a very accurate material model is required, performing well for a huge variety of different geometrical characteristics. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model the behaviour of polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. Through homogenisation and optimisation techniques, effective stress-strain curves are determined and can be compared to results from real forming processes leading to a suitable effective material model.
TL;DR: In this paper, a nonlocal cohesive zone model (CZM) for finite thickness interfaces was used to describe the phenomenon of grain boundary separation, considering the dependency of the grain boundary thickness on the grain size observed in polycrystals, a distribution of interface thicknesses was obtained.
Abstract: In this paper, the phenomenon of intergranular fracture in polycrystalline materials is investigated using a nonlinear fracture mechanics approach. The nonlocal cohesive zone model (CZM) for finite thickness interfaces recently proposed by the present authors is used to describe the phenomenon of grain boundary separation. From the modelling point of view, considering the dependency of the grain boundary thickness on the grain size observed in polycrystals, a distribution of interface thicknesses is obtained. Since the shape and the parameters of the nonlocal CZM depend on the interface thickness, a distribution of interface fracture energies is obtained as a consequence of the randomness of the material microstructure. Using these data, fracture mechanics simulations are performed and the homogenized stress-strain curves of 2D representative volume elements (RVEs) are computed. Failure is the result of a diffuse microcrack pattern leading to a main macroscopic crack after coalescence, in good agreement with the experimental observation. Finally, testing microstructures characterized by different average grain sizes, the computed peak stresses are found to be dependent on the grain size, in agreement with the trend expected according to the Hall-Petch law.
01 Jan 2011
TL;DR: A concurrent two-scale approach for frictional non-cohesive granular materials is presented in which the virtual work is interpolated between both models and compatibility is assured by kinematic constraints.
Abstract: A concurrent two-scale approach for frictional non-cohesive granular materials is presented. In domains of large deformation the material is modeled on the grain scale by a 3D discrete element method. Elsewhere the material is considered continuous and modeled by the finite element method using a non-associative Mohr-Coulomb model whose parameters are fit to the particle model via a homogenization scheme. The discrete and finite element model are coupled by the Arlequin method. Therefore an overlapping domain is introduced in which the virtual work is interpolated between both models and compatibility is assured by kinematic constraints. For this purpose the discrete particle displacements are split into a fine and coarse scale part and equality of the coarse scale part and the continuum solution is enforced through the penalty method.
01 Jan 2011
TL;DR: In this article, the authors investigate the stressing and the deformations of elastic structures subjected to applied loads, and restrict themselves to the simplest structural members, namely, bars under tension or compression.
Abstract: Objectives: In this textbook about the Mechanics of Materials we investigate the stressing and the deformations of elastic structures subjected to applied loads. In the first chapter we will restrict ourselves to the simplest structural members, namely, bars under tension or compression.
01 Jan 2011
TL;DR: In this paper, a new formulation for the quadrilateral is presented, where the standard bilinear element shape functions are expanded about the element center into a Taylor series in the physical co-ordinates.
Abstract: A new formulation for the quadrilateral is presented. The standard bilinear element shape functions are expanded about the element center into a Taylor series in the physical co-ordinates. Then the complete first order terms insure convergence with mesh refinement. Incompatible modes are added to the remaining higher order term, all of these being expanded into a second order Taylor series. The minimization of potential energy yields a constraint equation to eliminate the additional incompatible degrees of freedom on the element level. With the resulting constant and linear gradient operators being uncoupled, the stiffness matrix is written in terms of underintegration and stabilization. Therefore, the new quadrilateral is labeled QS6.
TL;DR: A scale adaptation strategy is developed for a more accurate analysis of generally inelastic macrostructures, where a transition from a homogenized description to an explicit micro-structural resolution is pursued.
Abstract: Analysing composite materials through efficient higher-order homogenization techniques requires accurate simulations of highly heterogeneous domains. However the validity of the homogenization response in regions with highly localized variations is still questionable. A scale adaptation strategy is developed for a more accurate analysis of generally inelastic macrostructures, where a transition from a homogenized description to an explicit micro-structural resolution is pursued. The designated zones of interest are indicated through two different methods of error estimation. First for mesh refinement approaches, the discretization error is estimated using an indicator developed by Zienkiewicz-Zhu and studying L2 norm. Furthermore a second adaptation zone is identified based on a post-processing step on the homogenized solution and corresponds to regions with high strain-gradients, the gradient of the deformation gradient. In the designated sub-domains a micro-structure representation will replace the homogenized area. The introduced scale-adaptivity method returns an inexpensive and more accurate analysis of composite materials. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
01 Jan 2011
TL;DR: In this article, a fictitious domain method is presented for the direct numerical modeling of 3D particulate flows, where the flow field is described by the nonstationary incompressible Navier-Stokes equations and the motion of the particles is modeled by the Newton-Euler equations.
Abstract: In this work a fictitious domain method is presented for the direct numerical modeling of 3D particulate flows. The flow field is described by the nonstationary incompressible Navier-Stokes equations and the motion of the particles is modeled by the Newton-Euler equations. For the computation of the two-phase flow the multigrid Finite Element Method (FEM) is coupled with the Discrete Element Method (DEM). The phase coupling is performed in an explicit manner by applying rigid body motion constraints. The combination of fast FEM solvers with efficient search algorithms for the DEM allows 3D simulations with a large number of particles.
TL;DR: In this article, the model of concrete deterioration due to the alkali silica reaction (ASR) at the micro-scale 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 the hardened cement paste (HCP) and computational homogenization of damage are addressed.
Abstract: In this contribution, the model of the concrete deterioration due to the 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 the hardened cement paste(HCP) and computational homogenization of damage are addressed in this contribution. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
01 Jan 2011
TL;DR: In this article, ausschlieslich mit der statischen Stabilitat elastischer tragwerke. Butt et al. beschaftigen uns in diesem Kapitel ausschtliche mit der Statischen Strobilitatsproblem es sich im konkreten Fall handelt.
Abstract: Der Begriff der Stabilitat wird im alltaglichen und im technischen Sprachgebrauch vielfaltig verwendet. Man muss daher stets genau angeben, um welches spezielle Stabilitatsproblem es sich im konkreten Fall handelt. Wir beschaftigen uns in diesem Kapitel ausschlieslich mit der statischen Stabilitat elastischer Tragwerke.
01 Jan 2011
TL;DR: In Band 2 as mentioned in this paper, die Grundlagen der linearen Elastizitatstheorie zusammengestellt werden, sollen hier the Grund lagen der Elastostatik zusammenengestehen.
Abstract: In Band 2 haben wir uns schon mit Problemen der Elastostatik befasst, wobei wir uns dort im wesentlichen auf die Untersuchung von Staben und Balken beschrankt haben. Um weitergehende Fragen behandeln zu konnen, sollen hier die Grundlagen der linearen Elastizitatstheorie zusammengestellt werden. Das Beiwort „linear“ deutet dabei an, dass sich diese Theorie auf das linear-elastische Stoffgesetz sowie auf kleine (infinitesimale) Verzerrungen beschr ankt. Hinsichtlich der praktischen Anwendung wird hierdurch ein groser Bereich von Ingenieurproblemen abgedeckt.
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TL;DR: Within this study a finite element program was developed that allows for fast contact detection of multiple deformable bodies and is able to automatically introduce new surfaces for cracks and the parts being cut out.
Abstract: Processes in which localizations lead to fracture are common for brittle materials. To simulate these problems methods have to be designed that allow for crack detection and propagation. Within this study a finite element program was developed that allows for fast contact detection of multiple deformable bodies and is able to automatically introduce new surfaces for cracks and the parts being cut out. Within the simulation inertial effects have to be considered that occur during the time dependent solution process. Due to the complexity of the simulations, a new open software tool was developed.
01 Jan 2011
TL;DR: In this article, a finite deformation homogenization framework is developed to predict the macroscopic thermal response of contact interfaces between rough surface topographies, and the homogenized contact response effectively predicts a temperature jump across the macroscale contact interface.
Abstract: A finite deformation homogenization framework is developed to predict the macroscopic thermal response of contact interfaces between rough surface topographies. The overall homogenization framework transfers macroscopic contact variables such as surfacial stretch, pressure and heat flux as boundary conditions on a test sample within a micromechanical interface testing procedure. An analysis of the thermal dissipation within the test sample reveals a thermodynamically consistent identification for the macroscopic thermal contact conductance parameter that enables the solution of a homogenized thermomechanical contact boundary value problem based on standard computational approaches. The homogenized contact response effectively predicts a temperature jump across the macroscale contact interface.