Circumventing the volume and contact constraints in multiphysics finite element simulations

Abstract

We consider two multiphysics problems in geomechanics with constraints. The first involves coupled solid deformation–fluid diffusion subject to a volume constraint in the limit of no-flow. The second is the classic contact problem subject to a no-interprenetration constraint. Both problems are known to generate unphysical oscillation in the pressure field when some combinations of displacement and pressure finite element interpolations are employed. We trace the problem to the non-satisfaction of the LBB condition and utilize a stabilization technique based on polynomial pressure projection to circumvent the unpreferable pressure oscillation.