Implicit dynamic three-dimensional finite element analysis of an inelastic biphasic mixture at finite strain: Part 1: Application to a simple geomaterial

Based on the mixture theory formulation for a fluid-saturated, inelastic, pressure-sensitive porous solid subjected to dynamic large strain deformation, a 3D finite element implementation with implicit time integration is presented. A recently published 2D implementation [Li et al. 2004, CMAME, v193, p3837–70] is extended to 3D, porosity-dependent permeability, and pressure-sensitive inelastic solid skeleton response at finite strain. The Clausius-Duhem inequality provides the form of the constitutive equations for the solid and fluid phases, as well as the dissipation function. A non-associative Drucker-Prager cap-plasticity model at finite strain is formulated based on a multiplicative decomposition of the deformation gradient, and numerically integrated semi-implicitly in the intermediate configuration to avoid questions of incremental objectivity. The elastic implementation is verified with available 1D analytical and 2D benchmark problems. New numerical solutions for 3D large strain dynamic behavior of saturated inelastic porous media are presented. The computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated.