Morphological representative pattern-based bounding inelasticity

Michel Bornert (1) , Claude Stolz (1) , André Zaoui (1)

1 LMS - Laboratoire de mécanique des solides

A general theory for the homogenization of heterogeneous linear elastic materials that relies on the concept of morphological representative pattern is given. It allows the derivation of rigorous bounds for the effective behaviour of the Voigt-Reuss type, which apply to any distribution of patterns, or of Hashin-Shtrikman-type, which are restricted to materials whose pattern distributions are isotropic. Particular anisotropic distributions of patterns can also be considered : Hashin-Shtrikman-type bounds for anisotropic media are then generated. The resolution of the homogeneization problem leads to a complex composite inclusion problem with no analytical solution in the general case. Here it is solved by numerical procedure basedon the finite element method. As an example of possible application, this procedure is used to derive new bounds for matrix-inclusion composites with cubic symmetry as well as for transversely isotropic materials.

Domaines: Mécanique des matériaux [physics.class-ph]; Physique Numérique [physics.comp-ph]

Michel Bornert, Claude Stolz, André Zaoui. Morphological representative pattern-based bounding inelasticity. Journal of the Mechanics and Physics of Solids, 1996, 44 (3), pp.307-331. ⟨10.1016/0022-5096(95)00083-6⟩. ⟨hal-00092045⟩