Finite element modeling of spherical indentation in a poro‐elasto‐plastic medium via step displacement loading

A hydromechanically coupled finite element method (FEM) algorithm following a mixed continuous Galerkin formulation for displacement and pore pressure is adopted for modeling of spherical indentation in a poro‐elasto‐plastic medium. The fully saturated porous medium is assumed to be isotropic and elasto‐perfectly plastic, obeying a Drucker‐Prager yield criterion with an associative or non‐associative flow rule. The Newton‐Raphson method with the tangent stiffness scheme is employed to deal with plasticity in the solid skeleton. A stabilization scheme, which permits equal‐order interpolation for the displacement and pore pressure fields and suppresses pore pressure oscillation in the incompressible or nearly incompressible limit, is incorporated in this FEM algorithm. The FEM algorithm is extensively benchmarked with poroelastic analytical solutions to the problems of Terzaghi, Mandel, Cryer, and De Leeuw and an analytic solution for one‐dimensional poro‐elasto‐plastic consolidation. Numerical simulations of poroelastic spherical indentation via step displacement loading are conducted to show that the normalized indentation force as a function of dimensionless time has only relatively weak dependence on material properties through a single derived parameter ω . Such universality is shown for three types of surface drainage conditions. For indentation in a poro‐elasto‐plastic medium, it is shown that even though plasticity occurs immediately at the undrained limit, if cohesion is within a certain range, there is no plastic strain accumulation during the transient period and the normalized force relaxation behavior could be approximated as poroelastic.