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

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.