Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method
01 Mar 1995-Computer Methods in Applied Mechanics and Engineering (North-Holland)-Vol. 121, pp 373-409
TL;DR: In this article, a Voronoi cell finite element method is developed to solve small deformation elastic-plasticity problems for arbitrary heterogenous materials, which is based on Dirichlet Tessellation of microstructural representative materials.
About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1995-03-01. It has received 240 citations till now. The article focuses on the topics: Centroidal Voronoi tessellation & Voronoi diagram.
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TL;DR: In this article, a quantitative definition of the representative volume element (RVE) size is proposed, which can be associated with a given precision of the estimation of the overall property and the number of realizations of a given volume V of microstructure that one is able to consider.
1,772 citations
Cites methods from "Elastic-plastic analysis of arbitra..."
...Note that Ghosh and Moorthey(1995) developed a finite element method based on Vorono€ ii cells....
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TL;DR: In this article, the convergence of the macroscopic field variables on the selected size of unit cells is studied quantitatively via the computational homogenization method, and the convergence nature of microscopic stress values is quantitatively through the computation homogenisation method.
521 citations
TL;DR: In this article, a review of multiscale methods for modeling mechanical and thermomechanical responses of composites is presented, both at the material level and at the structural analysis level.
Abstract: Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.
489 citations
TL;DR: In this paper, a method for rendering ordinary beam-spring networks elastically uniform is also given for predicting brittle fracture in homogeneous, isotropic materials, based on Voronoi diagrams with random geometry.
476 citations
TL;DR: In this article, a two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements, which can be unified in association with the homogenization procedure for general nonlinear problems.
434 citations
References
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TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Abstract: It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.
11,784 citations
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Abstract: Variational principles in the linear theory of elasticity, involving the elastic polarization tensor, have been applied to the derivation of upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry. When the ratios between the different phase moduli are not too large the bounds derived are close enough to provide a good estimate for the effective moduli. Comparison of theoretical and experimental results for a two-phase alloy showed good agreement.
5,224 citations
Book•
01 Jan 1982TL;DR: In this paper, the authors present numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals using double kink mechanisms for discrete dislocations in BCCs.
Abstract: Preface Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals Microstructure and stray electric fields at surface cracks in ferroelectrics Double kink mechanisms for discrete dislocations in BCC crystals The expanding spherical inhomogeneity with transformation strain A new model of damage: a moving thick layer approach On configurational forces at boundaries in fracture mechanics HotQC simulation of nanovoid growth under tension in copper Coupled phase transformations and plasticity as a field theory of deformation incompatibility Continuum strain-gradient elasticity from discrete valence force field theory for diamond-like crystals
4,951 citations
TL;DR: In this article, the elastic moduli of two-phase composites are estimated by a method that takes account of the inhomogeneity of stress and strain in a way similar to the Hershey-Kroner theory of crystalline aggregates.
Abstract: T he macroscopic elastic moduli of two-phase composites are estimated by a method that takes account of the inhomogeneity of stress and strain in a way similar to the Hershey-Kroner theory of crystalline aggregates. The phases may be arbitrarily aeolotropic and in any concentrations, but are required to have the character of a matrix and effectively ellipsoidal inclusions. Detailed results arc given for an isotropic dispersion of spheres.
3,289 citations
Book•
01 Jul 1993TL;DR: In this paper, the authors introduce basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary value problems and extremum principles three-dimensional problems solution of singular problems.
Abstract: Part 1 Overall properties of heterogeneous solids: aggregate properties and averaging methods aggregate properties, averaging methods elastic solids with microcavities and microcracks linearly elastic solids, elastic solids with traction-free defects, elastic solids with micrcavities, elastic solids with microcracks elastic solids with micro-inclusions overall elastic modulus and compliance tensors, examples o elastic solids with elastic micro-inclusions, upper and lower bounds for overall elastic moduli, self-consistent differential and related averaging methods, Eshelby's tensor and related topics solids with periodic microstructure general properties and field equations, overall properties of solids with periodic microstructure, mirror-image decomposition of periodic fields. Part 2 Introduction to basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary-value problems and extremum principles three-dimensional problems solution of singular problems. Appendix: references.
2,544 citations