A three-field (displacement–pressure–concentration) formulation for coupled transport–deformation problems

This paper provides a three-field finite element formulation for the evaluation of coupled transport–deformation problems. A stabilized advection–diffusion–reaction model is employed to idealize the mass transport of an aggressive environmental agent within a solid medium, whereas the deformation response of the medium is formulated using the mixed finite element approach with pressure and displacement as unknown variables. The proposed model accurately captures the pressure and pressure gradient fields that characterize the reaction and advection terms of the mass transport model. The concentration-dependent viscoplastic deformation response is idealized using a generalized Johnson–Cook plasticity model. The accuracy characteristics of the proposed three-field formulation are assessed by numerical simulations, which indicate the significance of accurate estimation of pressure at high stress gradient zones for correct characterization of mass transport.