A gradient theory of porous elastic solids

Abstract

AbstractThis paper is concerned with a theory of elastic materials with voids where the second gradient of deformation and the second gradient of volume fraction field are added to the set of independent constitutive variables. First, we establish the nonlinear theory and study the continuous dependence of solutions upon initial state and body loads. Then, we derive the linear theory and establish a uniqueness theorem with no definiteness assumption on the constitutive coefficients. We present the equations for homogeneous and isotropic solids and establish a counterpart of the Boussinesq‐Somigliana‐Galerkin solution in the classical elastostatics. The effects of concentrated body loads acting in an infinite space are investigated.