A fully coupled diffusional-mechanical formulation: numerical implementation, analytical validation, and effects of plasticity on equilibrium

A macroscopic coupled stress-diffusion theory which accounts for the effects of nonlinear material behaviour, based on the framework proposed by Cahn and Larché, is presented and implemented numerically into the finite element method. The numerical implementation is validated against analytical solutions for different boundary valued problems. Particular attention is payed to the open system elastic constants, i.e. those derived at constant diffusion potential, since they enable, under circumstances, the equilibrium composition field for any generic chemical-mechanical coupled problem to be obtained through the solution of an equivalent elastic problem. Finally, the effects of plasticity on the overall equilibrium state of the coupled problem solution are discussed.