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

TL;DR

This paper introduces a coupled deformation-diffusion model for elastic solids, with a novel numerical method ensuring non-negative concentrations, and demonstrates its effectiveness through numerical examples highlighting the impact of coupling on material degradation and healing.

Contribution

It presents a new computational framework for coupled deformation-diffusion problems that guarantees non-negative concentrations and systematically studies the effects of coupling on material behavior.

Findings

The proposed numerical method prevents unphysical negative concentrations.

Coupled deformation-diffusion significantly alters material response compared to uncoupled models.

Numerical examples confirm robustness and convergence of the framework.

Abstract

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framework for solving the proposed mathematical model, which consists of coupled non-linear partial differential equations. It should be noted that many popular numerical formulations may produce unphysical negative values for the concentration, particularly, when the diffusion process is anisotropic. The violation of the non-negative constraint by these numerical formulations is not mere numerical noise. In the proposed computational framework we employ a novel numerical formulation that will ensure that the concentration of the diffusant be 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. Another contribution of this paper is to systematically study the affect of transport of the diffusant on the deformation of the solid and vice-versa, and their implication in modeling degradation/healing of materials. We show that the coupled response is both qualitatively and quantitatively different from the uncoupled response.