Analysis and numerical simulation of strong discontinuities in finite strain poroplasticity

Abstract

This paper presents an analysis of strong discontinuities in coupled poroplastic media in the finite deformation range. A multi-scale framework is developed for the characterization of these solutions involving a discontinuous deformation (or displacement) field in this coupled setting. The strong discontinuities are used as a tool for the modeling of the localized dissipative effects characteristic of the localized failures of typical poroplastic systems. This is accomplished through the inclusion of a cohesive-frictional law relating the resolved stresses on the discontinuity and the accumulated fluid content on it with the displacement and fluid flow jumps across the discontinuity surface. The formulation considers the limit of vanishing small scales, hence recovering a problem in the large scale involving the usual regular displacement and pore pressure variables, while capturing correctly these localized dissipative mechanisms. All the couplings between the mechanical and fluid problems, from the modeling of the solid's response through effective stresses and tractions to the geometric coupling consequence of the assumed finite deformation setting, are taken into account in these considerations. The multi-scale structure of the theoretical formulation is fully employed in the development of new enhanced strain finite elements to capture these discontinuous solutions with no regularization of the singular fields appearing in the formulation. Several numerical simulations are presented showing the properties and performance of the proposed localized models and the enhanced finite elements used in their numerical implementation.