Journal ArticleDOI
Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method
Somnath Ghosh,Suresh Moorthy +1 more
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TLDR
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.read more
Citations
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Polygon scaled boundary finite elements for crack propagation modelling
TL;DR: An automatic crack propagation modelling technique using polygon elements is presented in this article, where a simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks.
Journal ArticleDOI
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
TL;DR: In this article, a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries is presented, where grain boundaries and junctions are inserted into finite elements by exploiting the partition of unity property of finite element shape functions.
Journal ArticleDOI
Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping
TL;DR: Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.
Journal ArticleDOI
Quantitative characterization and modeling of composite microstructures by voronoi cells
TL;DR: In this article, Voronoi cells resulting from Dirichlet tessellation of a planar heterogeneous microstructure are introduced as a unified tool in characterization and response modeling of multiphase materials.
Journal ArticleDOI
New perspectives on polygonal and polyhedral finite element methods
TL;DR: This paper first presents an overview of previous developments on conforming polygonal and polyhedral finite elements, and then appeals to the exact decomposition in the VEM to obtain a robust and efficient generalized barycentric coordinate-based Galerkin method on polygonnal andpolyhedral elements.
References
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Journal ArticleDOI
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
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.
Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
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.
Book
Micromechanics of defects in solids
Toshio Mura,D. M. Barnett +1 more
TL;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.
Journal ArticleDOI
A self-consistent mechanics of composite materials
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.
Book
Micromechanics: Overall Properties of Heterogeneous Materials
TL;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.
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