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This paper deals with the formulation and numerical implementation of a fullycoupled continuum model for deformation-diffusion in linearized elastic solids.The mathematical model takes into account the effect of the deformation on thediffusion process, and the affect of the transport of an inert chemical specieson the deformation of the solid. We then present a robust computationalframework for solving the proposed mathematical model, which consists ofcoupled non-linear partial differential equations. It should be noted that manypopular numerical formulations may produce unphysical negative values for theconcentration, particularly, when the diffusion process is anisotropic. Theviolation of the non-negative constraint by these numerical formulations is notmere numerical noise. In the proposed computational framework we employ a novelnumerical formulation that will ensure that the concentration of the diffusantbe always non-negative, which is one of the main contributions of this paper.Representative numerical examples are presented to show the robustness,convergence, and performance of the proposed computational framework. Anothercontribution of this paper is to systematically study the affect of transportof the diffusant on the deformation of the solid and vice-versa, and theirimplication in modeling degradation/healing of materials. We show that thecoupled response is both qualitatively and quantitatively different from theuncoupled response.

A framework for coupled deformation-diffusion analysis with application to degradation/healing