Three-dimensional numerical manifold formulation with continuous nodal gradients for dynamics of elasto-plastic porous media

A three-dimensional (3D) numerical manifold formulation with continuous nodal gradients (H8-CNS) is presented for dynamic analysis of saturated elasto-plastic porous media based on the three-variable (u−w−p) formulation. Using meshes of 8-node hexahedra as mathematical patches, the skeleton displacement (u) and fluid velocity (w) interpolations are constructed with a constrained and ortho-normalized least-squares (CO-LS) scheme and a piecewise constant interpolation for fluid pressure field is employed. One feature of H8-CNS is to overcome locking in both limiting cases of low permeability and rigid skeleton. Another feature of H8-CNS is to achieve higher accuracy in stress results for porous media problems involving both elastic and elasto-plastic skeleton behaviors. H8-CNS is also able to fully capture dynamic responses of porous media under high-frequency loading. The accuracy and stability of H8-CNS are verified by performing a variety of numerical simulations. Time integration of H8-CNS is shown to be stable and accurate using the energy balance condition. •A 3D NMM H8-CNS is given for dynamics of elasto-plastic porous media.•For elastic/plastic analysis, H8-CNS gives more accurate stress than mixed FEM.•H8-CNS is immune from locking.