Mixed finite element method for saturated poroelastoplastic media at large strains

A mixed nite element for hydro-dynamic analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, e ective stresses, strains for the solid phase and pressure, pressure gradients, and Darcy velocities for the uid 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- eld 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 uid phases within the element are assumed independently. The proposed mixed nite 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 sti ness 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