On finite strain poroplasticity with reversible and irreversible porosity laws. Formulation and computational aspects

• A nonlinear porosity formulation at finite strain and high pore pressure is proposed.
• Total reversible as well as partial irreversibility of the porosity are proposed.
• The laws are integrated in a sound thermodynamic framework of open media.
• Finite strain poroplasticity is considered within a detailed finite element framework.
• A staggered scheme is used and numerical simulations are shown with parametric studies.

The main purpose of this paper is the formulation of a poroplastic framework suitable for finite strain and high pore pressure in saturated porous media. Here we make a distinction between poroplasticity with totally reversible porosity and poroplasticity with the occurrence of irreversible porosity. For this latter, an important key point is that the total porosity is not additively decomposed as usual into reversible and irreversible parts. As shown, the permanent porosity is embedded into the definition of the total porosity itself. The approach is built around the physical restriction that the actual Eulerian porosity is bounded in the interval [0, 1] for any admissible process. Elementary considerations motivate the modeling throughout the paper and the formulation is integrated within the unified continuum thermodynamics of open media, which is crucial in setting the convenient forms of the state laws and evolution equations for the flux variables to fully characterize the behavior of porous materials. On the numerical side, the algorithmic design is described in detail for an easy implementation within the context of the finite element method. Finally, we present a set of numerical simulations to illustrate the effectiveness of the proposed framework.