Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media

Vincent Pensée (1) , Qi-Chang He (1)

1 LaM - Laboratoire de Mécanique

Under investigation is a heterogeneous material consisting of an elastic homogeneous isotropic matrix in which layered elastic isotropic inclusions or pores are embedded. The generalized self-consistent model (GSCM) is extended so as to be capable of estimating the apparent elastic properties of a finite-size specimen smaller than a representative volume element (RVE). The kinematical or static apparent shear modulus is determined as a root of a cubic polynomial equation instead of a quadratic polynomial equation as in the classical GSCM of Christensen and Lo [Christensen, R.M., Lo, K.H., 1979. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315-330]. It turns out that the extended GSCM establishes a link between the composite sphere assemblage model (CSAM) of Hashin [Hashin, Z., 1962. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29, 143-150] and the classical GSCM. Demanding that the normalized distance between the kinematical and static apparent moduli of a finite-size specimen be smaller than a certain tolerance, the minimum RVE size is estimated in a closed form. (c) 2006 Elsevier Ltd. All rights reserved.

Domaines: Mécanique [physics.med-ph]

Vincent Pensée, Qi-Chang He. Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media. International Journal of Solids and Structures, 2007, 44 (7-8), pp.2225--2243. ⟨10.1016/j.ijsolstr.2006.07.003⟩. ⟨hal-00693619⟩