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.

New Lie Symmetries and Exact Solutions of a Mathematical Model Describing Solute Transport in Poroelastic Materials

“…A typical biological example is the glucose solute penetrating a tissue layer. The basic theory of poroelasticity was developed by Biot [1] and its state-ofthe-art can be found in the well-known books [1][2][3] (see also recent studies, e.g., [4][5][6][7][8]). A poroelastic material is considered as the superposition of two continuous media: the matrix (skeleton), occupying the fractional volume θ M , and the system of pores saturated by a fluid, occupying the fractional volume θ F (θ F + θ M = 1).…”