A simple solution strategy for coupled piezo-diffusion in elastic solids

In this work, a simple solution strategy for the fully coupled problem of the diffusion of a mobile constituent into an elastic solid is proposed. The key features of the proposed solution strategy are a superconvergent strain recovery and a final stress filtering, suitably arranged with a standard recursive staggering scheme. The strategy is devised to overcome some shortcomings arising when solving the problem within the standard finite element framework and can be easily implemented by using existing finite element packages for uncoupled elasticity and diffusion problems. Numerical applications show the effectiveness of the proposed solution strategy.