Formulation of a nonlinear porosity law for fully saturated porous media at finite strains

In this work, we develop a mathematical formulation of a nonlinear porosity law suitable for finite strain and high pore pressure conditions in porous media. The approach is built around the physical restriction that, by definition, the actual porosity is bounded in the interval [0,1] for any admissible process. Specifically, the model is motivated by elementary considerations that have been extended to the nonlinear range and, at the limiting case of an infinitesimal approximation, it reaches the porosity law of the classical linear poromechanics. In a next step, the formulation is integrated within the unified framework of continuum thermodynamics of open media which is crucial in setting the convenient forms of the constitutive relations and evolution equations to fully characterize the behavior of porous materials. Finite strain poroelasticity as well as poroplasticity are considered in this work where, furthermore, a generalized constitutive law for the saturating fluid has been introduced such that both the incompressible fluid and ideal gas are embedded as particular cases. Parametric studies are conducted throughout the paper by means of simulated hydrostatic compression tests to highlight the effectiveness of the present modeling framework.