Matériaux cellulaires aux propriétés de transport et mécanique optimales

Abstract

Optimal upper bounds on the average conductivity and the bulk modulus of low density cellular materials are established. These bounds are tighter than the classical Hashin-Shtrikman upper bounds, and can be applied to anisotropic materials. Furthermore, necessary and sufficient conditions on the microgeometry of the cellular materials to maximize(for a given solid volume fraction) either the average conductivity or the bulk modulus are derived. The conditions are found to be identical for both quantities, so that the bounds are attained simultaneously: a low-density cellular material with maximal average conductivity will have maximal bulk modulus as well.