Effects of stress-diffusion interactions in an isotropic elastic medium in the presence of geometric discontinuities

The role of geometric discontinuities on stress-diffusion interactions in an elastic medium is studied using a fully coupled chemo-mechanical framework. The two-way coupled framework entails the dependence of stress on the local concentration and the flux on the gradient of the hydrostatic stress. The transient, coupled nonlinear system of differential equations is solved using the finite element method. The results from the two-way framework are compared with solutions obtained when only stress depends on the concentration (one-way coupled). It is found that the time to reach steady state is lower for the fully coupled case. Furthermore, the fully coupled approach predicts a non-uniform concentration distribution at steady state in contrast to one-way coupled system. The shape of the discontinuities and their relative positions in the domain are found to influence the concentration and the stress fields significantly. The maximum stress concentration factor reached before the steady state is over predicted by the one-way coupled model. This observation suggests that better optimal design may be possible when two-way models are used.