Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions Original Research Article

In this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro-plasticity. Fully saturated conditions are assumed. The model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts, together with an additive elastoplastic decomposition of the fluid content. The final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation. The particular case of an associated Drucker-Prager model in effective stresses is considered as a model example. A complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate. We describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem. Finally, we present representative numerical simulations to illustrate the features of the proposed models. In particular, the case of strain localization in globally undrained conditions is studied in the proposed framework.