Mechanically driven mass diffusion in elastic solids

The work focuses on the coupled problem of the diffusion of a mobile fluid constituent into an elastic solid. A complete set of governing equations of the problem is proposed and can be derived operating within the framework of the modern thermodynamics of irreversible processes. The formulation takes properly into account for the full coupling between the mechanical and the diffusive behaviour. The most used tool for the numerical analysis of this phenomenon is the standard finite element method, based on assumed displacement and concentration fields. This approach can lead to some unexpected results, such as lack of convergence of the solution in terms of diffusive variables and anomalous oscillations of the resultant stress distribution. To overcome these shortcomings while remaining in the standard finite element framework, a recovery-based solution strategy is devised. It is based on a recursive staggering scheme suitably combined with an intermediate superconvergent strain recovery and a final stress filtering. The proposed procedure can be easily implemented by using existing finite element packages for uncoupled elasticity and uncoupled diffusivity problems. Numerical applications show the effectiveness of the proposed solution strategy.