  The modeling of coupled fluid transport and deformation in a porous medium is
essential to predict the various geomechanical process such as CO2
sequestration, hydraulic fracturing, and so on. Current applications of
interest, for instance, that include fracturing or damage of the solid phase,
require a nonlinear description of the large deformations that can occur. This
paper presents a variational energy-based continuum mechanics framework to
model large-deformation poroelasticity. The approach begins from the total free
energy density that is additively composed of the free energy of the
components. A variational procedure then provides the balance of momentum,
fluid transport balance, and pressure relations. A numerical approach based on
finite elements is applied to analyze the behavior of saturated and unsaturated
porous media using a nonlinear constitutive model for the solid skeleton.
Examples studied include the Terzaghi and Mandel problems; a gas-liquid
phase-changing fluid; multiple immiscible gases; and unsaturated systems where
we model injection of fluid into soil. The proposed variational approach can
potentially have advantages for numerical methods as well as for combining with
data-driven models in a Bayesian framework.
