Continuum Micromechanics: Survey

By A. Zaoui. 2002

681 citations recorded by the source corpus.

The foundations of classical homogenization techniques, which aim at predicting the overall behavior of heterogeneous materials from that of their constituents, are reviewed. After introductory definitions and a methodological preamble, attention is focused on linear elasticity, for which the basic principles of estimating and bounding the overall properties are introduced and illustrated. In this context, special recourse is made for that to the solution of the inclusion and inhomogeneity problems as reported by Eshelby in 1957. Approaches proposed recently to account in a better way for the structural morphology of the considered materials are briefly mentioned. The case of linear elasticity with eigenstrains is then discussed: several applications, including heterogeneous thermoelasticity, can be investigated within this framework. Finally, outlines of nonlinear micromechanics are briefly reported from a historical point of view: from rate-independent elastoplasticity to nonlinear elasticity and viscoplasticity, examples of a fruitful interaction between the search for new estimates and the derivation of rigorous bounds are given and the crucial question of the description of intraphase heterogeneity is emphasized. Viscoelastic coupling and rate-dependent effects are briefly discussed in conclusion.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d00a33c97ff3680573e0c17b40fc595ccfbc37b1

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In Mechanics of Materials

Citations in the corpus

Mechanical properties of open-cell metallic biomaterials manufactured using additive manufacturing (2013, positive): “of ellipsoidal inclusions [14–17] was used.”
The nano-mechanical signature of Ultra High Performance Concrete by statistical nanoindentation techniques (2008, methodology): “To do so, we use the classical tools of linear continuum micromechanics, namely the strain localization relations [42,43]:”
A micromechanical approach to the strength criterion of Drucker‐Prager materials reinforced by rigid inclusions (2004, background): “The micromechanical approach to the response of composites in the non-linear domain is more recent and several important issues are still open [2].”
The effect of the nanogranular nature of shale on their poroelastic behavior (2007, methodology): “Their size is typically above the micrometer size, thus satisfying the scale separability condition required for the application of micromechanics theory [ 83 ].”
Effective Permeability of Media with a Dense Network of Long and Micro Fractures (2009, methodology): “The framework of random media upscaling, which is also commonly used to estimate mechanical effective properties [Zaoui, 2002], is considered here so as to provide a methodology based on the self-consistent scheme to estimate the effective permeability Khom in the general case of a 3D anisotropic…”
Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, background): “The affine formulation of Masson et al. (2000) is an interesting alternative to Hill’s formulation (see also (Zaoui, 2002)).”
Micromechanical investigation of Portland cement paste (2014, background): “Within the framework of micromechanics [47], the ‘macroscopic’ stress P and strain X of REV (representative elementary volume) are described as the averages of the stress field r(x) and strain field e(x) of REV: X 1⁄4 hrðxÞiV ; X 1⁄4 heðxÞiV ð16Þ”
Microstructure-based micromechanical prediction of elastic properties in hydrating cement paste (2006, background): “A lot of literature deals with the theory of homogenization, a brief review is given in, e.g., [27, 32 ].”