A simple framework for arriving at bounds on effective moduli in heterogeneous anisotropic poroelastic solids

TL;DR

This paper introduces a framework that derives bounds on the effective elastic moduli of heterogeneous anisotropic poroelastic materials using modified boundary conditions and the concept of representative volume elements.

Contribution

It proposes a novel approach replacing traditional boundary conditions with pressure and fluid content conditions to establish bounds on poroelastic moduli.

Findings

Derived upper and lower bounds on effective moduli.

Validated bounds are representative of the entire heterogeneous solid.

Framework applicable to anisotropic poroelastic materials.

Abstract

The concepts of representative volume element (RVE), statistical homogeneity and homogeneous boundary conditions are invoked to arrive at bounds on effective moduli for heterogeneous anisotropic poroelastic solids. The homogeneous displacement boundary condition applicable to linear elasticity is replaced by a homogeneous displacement-pressure boundary condition to arrive at an upper bound within the RVE while the homogeneous traction boundary condition applicable to linear elasticity is replaced by a homogeneous traction-fluid content boundary condition to arrive at a lower bound within the RVE. Statistical homogeneity is then invoked to argue that the bounds obtained over the RVE are representative of the bounds obtained over the whole heterogeneous poroelastic solid.