Mixed finite element method for saturated poroelastoplastic media at large strains

Abstract

AbstractA mixed finite element for hydro‐dynamic analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, effective stresses, strains for the solid phase and pressure, pressure gradients, and Darcy velocities for the fluid phase are interpolated as independent variables. The weak form of the governing equations of coupled hydro‐dynamic problems in saturated porous media within the element are given on the basis of the Hu–Washizu three‐field variational principle. In light of the stabilized one point quadrature super‐convergent element developed in solid continuum, the interpolation approximation modes for the primary unknowns and their spatial derivatives of the solid and the fluid phases within the element are assumed independently. The proposed mixed finite element formulation is derived. The non‐linear version of the element formulation is further derived with particular consideration of pressure‐dependent non‐associated plasticity. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elastoplastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non‐linearity, the co‐rotational formulation approach is used. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization due to strain softening in poroelastoplastic media subjected to dynamic loading at large strain. Copyright © 2003 John Wiley & Sons, Ltd.