Poromechanics approach for modeling closed-cell porous materials with soft matrices

The main purpose of this paper is the formulation of a modeling framework for closed-cell porous materials by means of the nowadays classical approach of poromechanics. The cavities being saturated with a single fluid phase, Biot’s theory drastically simplifies since no fluid diffusion is present in this case. Nevertheless, the fluid contribution to the macroscopic behavior is still present and the fluid mass conservation controls the pore pressure that contributes to the total stress at the macro-scale. A constitutive law for the saturating fluid is introduced that encompasses both ideal gas and incompressible fluids as particular cases. The approach is built around the unified framework of continuum thermodynamics which is crucial in setting the convenient form for the state laws. As the finite strain range is of concern, the modeling strongly depends on the Eulerian porosity law adopted in the spatial configuration. Two model examples are discussed with parametric studies to show the effectiveness of the proposed approach.