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American Society for Testing and Materials

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.

https://hal.archives-ouvertes.fr/hal-00111366/document

Continuum Micromechanics: Survey

A micromechanical analysis of the behavior of saturated elastic porous media is presented. Pores are connected and saturated with a fluid at uniform pressure. The non-linear macroscopic response of the porous medium is assumed to be related to the existence of a network of microcracks in the solid phase. The progressive closure of cracks during loading is viewed to control the material non-linearity. Using averaging schemes based on both the classical and modified secant methods, the non-linearity of the overall response is shown to be sometimes controlled by an effective stress. The modified secant method accounts in a certain way for the non-uniform distribution of strains within the solid phase. Different definitions of the effective stress are found, each of them being a combination of the overall stress with the fluid pressure. The hypothesis of connexion between pores and microcracks is discussed in details. The consequences of this hypothesis on the non-linear overall response are illustrated and comparisons are made with experimental data.

Micromechanical approach to the behavior of poroelastic materials

Damage observation and assessment of the Longxi tunnel during the Wenchuan earthquake

A micro–macro model for clayey rocks with a plastic compressible porous matrix

The present paper describes a micromechanics-based approach to the strength properties of composite materials with a Drucker–Prager matrix in the situation of non-associated plasticity. The concept of limit stress states for such materials is first extended to the context of homogenization. It is shown that the macroscopic limit stress states can theoretically be obtained from the solution to a sequence of viscoplastic problems stated on the representative elementary volume. The strategy of resolution implements a non-linear homogenization technique based on the modified secant method. This procedure is applied to the determination of the macroscopic strength properties and plastic flow rule of materials reinforced by rigid inclusions, as well as for porous media. The role of the matrix dilatancy coefficient is in particular discussed in both cases. Finally, finite element solutions are derived for a porous medium and compared to the micromechanical predictions.

Micromechanical approach to the strength properties of frictional geomaterials

https://hal-enpc.archives-ouvertes.fr/hal-01157363/document

Samir Maghous

Papers

Micromechanical approach to the strength properties of frictional geomaterials

Stability analysis of rock slopes subjected to seepage forces using the modified Hoek–Brown criterion

Bearing capacity of shallow foundations on rocks obeying a modified Hoek–Brown failure criterion

A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete

A model for in situ grouting with account for particle filtration