A note on the response of elastic bodies whose material moduli depend on the density and the mechanical pressure

Abstract

In this note we study the response of an inhomogeneous body, whose material moduli depend on the density and the mechanical pressure, that is described by an implicit constitutive relation between the Cauchy stress and the right Cauchy–Green tensor. Such a constitutive relation is relevant to the study of the deformation of porous elastic solids as the porous structure varies and the local density changes. The boundary value problems of a plate of such a material subject to uniaxial and bi-axial extension and compression are considered. We find that regions that are more porous, and thus of lower macroscopic density, have the propensity to fail than regions of higher density, in the sense the load carrying capacity decreases, when other measures such as the stress are comparable.