Couple-stress–based gradient theory of poroelasticity

Abstract

In this research, we present a gradient theory of poroelasticity based on the couple-stress. Within the context of finite deformations and in a thermodynamically consistent manner, the constitutive equations for the porous solid are derived by including the solid vorticity gradient and its power-conjugate counterpart, namely, the couple-stress. Subsequently, a linearized theory for an isotropic porous solid is developed in which two microstructure-dependent constitutive moduli (or equivalently, two material length-scale parameters) are introduced. To investigate the gradient effects on the responses of the material, the problem of wave propagation in fluid-saturated porous solids is formulated and solved based on the proposed theory. For comparison, the wave dispersion and attenuation curves are compared with those obtained from classical theory of poroelasticity.