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This paper has two objectives: (a) to formulate a mechanical theory of porous continua within the framework of strong discontinuity concept commonly employed for the analysis of strain localization in inelastic solids; and (b) to introduce an effective stress tensor for three-phase (solid-water-air) partially saturated porous continua emerging from principles of thermodynamics. To achieve the first objective, strong forms of the boundary-value problems are compared between two formulations, the first in which the velocity jump at the solid-fluid interface is treated as a strong discontinuity problem, and the second in which the strong discontinuity is smeared in the representative volume element. As for the second objective, an effective Cauchy stress tensor of the form r ¼ r þ ð1 À K=K s Þ p1 emerges from the formulation, where r is the total stress tensor, K and K s are the bulk moduli of the solid matrix and solid phase, respectively, and p is the mean pore water and pore air pressures weighted according to the degree of saturation. We show from the first and second laws of thermodynamics that this effective stress tensor is power-conjugate to the solid rate of deformation tensor, and that it includes the mechanical power required to compress the solid phase.

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We present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation. Momentum and mass conservation laws are written in Lagrangian form by a pull-back from the current configuration to the reference configuration following the solid matrix motion. A complete formulation based on the motion of the solid and fluid phases is first presented; then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so-called (v; p)-formulation, which is subsequently implemented in a finite element model. We show how the resulting finite element matrix equations can be consistently linearized, using a compressible neo-Hookean hyperelastic material with a Kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model. Numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures, as well as the strong convergence profile exhibited by the iterative algorithm.