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Representative elementary volume

About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.


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TL;DR: In this article, Monte Carlo simulations are used to obtain the first and second-order one-and two-point characteristics of these two random fields for random chessboards and matrix-inclusion composites.
Abstract: Department of Materials Science and Mechanics, Michigan State University, East Lansing MI 48824-1226 Many problems in solid and geomechanics require the concept of a meso-continuum, which allows a resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale. Passage from the microstructure to such a meso-continuum is based on a scale depen­dent window playing the role of a Representative Volume Element (RVE). It turns out that the material properties at the mesoscale cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields, corresponding to essential and natural boundary conditions on RVE, need to be introduced to bound the material response from above and from below. In this paper Monte Carlo simulations are used to obtain the first- and second-order one- and two-point characteristics of these two random fields for random chessboards and matrix-inclusion composites. Special focus is on the correlation functions describing the auto-covariances and crosscovariances of effective random meso-scale conductivity tensor Q; and its dual Sjj. Following issues are investigated: i) scale-dependence of noise-to-signal ratios of various components of Cy and Sjj, ii) spatial structure of the correlation function, iii) uniform strain versus exact calculations in determination of the correlation function, iv) correlation structure of compos­ites with inclusions without and with overlap. 1. INTRODUCTION One of the classical goals of micromechanics is the derivation of macroscopic properties on scales practically infinitely larger than the lengthscales at the microlevel. There are, how­ever, situations where description of material response at intermediate levels - so-called meso-level (or meso-scale) -is necessary. These are, for example, i) necessity to resolve local fields (of stress, say), ii) materials with spatially-depen­dent statistics, iii) solution of boundary value problems at macro-scales. Case i) is exemplified by almost any one of many problems in soil mechanics where a meso-scale has to be introduced to define a continuum over a granular mass in the first place (Ostoja-Starzewski, 1992). Case ii) is a situation where a pas­sage to an infinite scale would be beyond interest, such as for instance in a heterogenous interface problem (Ostoja-Starze­wski and Jasiuk, 1992; Jasiuk and Ostoja-Starzewski, 1994). A paradigm of case iii) is provided by so-called Stochastic Finite Elements (SFE) - a field of research developing over the past fifteen years, in which a micromechanical basis in set­ting up of a stochastic stiffness matrix is sorely needed (Ostoja-Starzewski, 1993a and 1993b). Most of the past research in SFE concerned linear elastic structural responses and relied on a straightforward generali­zation of Hooke's law (see e.g. Contreras, 1980; Liu, et al, 1986; Benaroya and Rehak, 1988; Shinozuka, 1988; Ghanem andSpanos, 1991), that is

60 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of local mechanical properties estimation in the real microstructure of WC/Co composite was addressed by using finite element analysis (FEA) to model the initial elastic and elastic-plastic response of WC and Co. The numerical results are in good agreement with published data for assessment of material properties and stress-strain behaviour.

60 citations

Journal ArticleDOI
TL;DR: In this article, the contribution of irregularly shaped inclusions into the effective moduli of two-dimensional elastic solids is calculated based on the analysis of a representative volume element subjected to a prescribed macrostress.

60 citations

Journal ArticleDOI
TL;DR: In this article, a pore-scale model for two-phase flow in dense packings of polydisperse spheres is introduced, where the pore space is decomposed by Regular Triangulation, from which a set of pores connected by throats are identified.

60 citations

Journal ArticleDOI
TL;DR: This work finds that xfem is the most suitable when the mesh if coarse, and methods based on Cartesian grids are best when a very fine mesh can be used, and Finite element methods are good compromises with high flexibility.

60 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023134
2022241
2021243
2020293
2019287
2018253