  The concept of representative volume element or RVE is invoked to develop an
algorithm for numerical homogenization of fluid filled porous solids. RVE based
methods decouple analysis of a composite material into analyses at the local
and global levels. The local level analysis models the microstructural details
to determine effective properties by applying boundary conditions to the RVE
and solving the resultant boundary value problem. The composite structure is
then replaced by an equivalent homogeneous material having the calculated
effective properties. We combine the features of two techniques: one is the
definition of a displacement field for the fluid phase to allow for a
definition of a continuous displacement field across the microstructure and the
other is the $FE^2$ numerical homogenization that couples the macroscale with
the RVE scale via gauss points.
