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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, the authors carried out a careful computational analysis of the effect of these two types of boundary conditions on the macroscopic response of the (idealized) porous solid and in particular, explored the sensitivity of the predicted response to the microscopic stress, void volume fraction and material non-linearity.
28 citations
TL;DR: In this article, the macrohomogeneity condition in the dynamic response of inhomogeneous micropolar (Cosserat) materials was determined, and the boundary loadings involved various combinations of average stresses and strains, along with couple-stresses and curvature tensors.
Abstract: We determine the macrohomogeneity (Hill-Mandel type) condition in the dynamic response of inhomogeneous micropolar (Cosserat) materials. The setting calls for small deformation gradients and curvatures, but without restrictions on the constitutive behavior and without any requirements of spatial periodicity. The condition gives admissible boundary loadings, along with extra terms representing kinetic energy contributions of both classical type and micropolar type. The said loadings involve various combinations of average stresses and strains, along with couple-stresses and curvature-torsion tensors. If applied to a specific microstructure in a computational mechanics approach, these boundary loadings will allow one to determine scale-dependent homogenization toward a representative volume element (RVE) of an equivalent homogeneous micropolar medium in either elastic or inelastic settings. By restricting the continuum model to an inhomogeneous Cauchy continuum and/or a quasi-static setting, the macrohomogeneity condition simplifies to conventional versions.
28 citations
TL;DR: In this article, a brief introduction to micromechanics using linear elastic materials as an example is provided, and detailed derivations of the rules of mixtures, and three full field MC theories including finite element analysis of a representative volume element (RVE analysis), mathematical homogenization theory (MHT), and mechanics of structure genome (MSG) are discussed.
Abstract: This article provides a brief introduction to micromechanics using linear elastic materials as an example. The fundamental micromechanics concepts including homogenization and dehomogenization, representative volume element (RVE), unit cell, average stress and strain theories, effective stiffness and compliance, Hill-Mandel macrohomogeneity condition. This chapter also describes the detailed derivations of the rules of mixtures, and three full field micromechanics theories including finite element analysis of a representative volume element (RVE analysis), mathematical homogenization theory (MHT), and mechanics of structure genome (MSG). Theoretical connections among the three full field micromechanics theories are clearly shown. Particularly, it is shown that RVE analysis, MHT and MSG are governed by the same set of equations for 3D RVEs with periodic boundary conditions. RVE analysis and MSG can also handle aperiodic or partially periodic materials for which MHT is not applicable. MSG has the unique capability to obtain the complete set of 3D properties and local fields for heterogeneous materials featuring 1D or 2D heterogeneities.
27 citations
TL;DR: In this article, a multi-point flux approximation method was used to predict the thermal conductivity of anisotropic materials based on the three-dimensional reconstruction of their fibrous structure, obtained from X-ray micro-tomography.
27 citations
TL;DR: In this article, a micromechanical model is used to investigate ply thickness effect on damage evolution of thin-ply carbon fiber reinforced laminate under transverse tensile load, and the results show that decreasing 90° lamina thickness alters damage progression mechanism and suppresses cracking within matrix loading.
27 citations