Variational multiscale enrichment for modeling coupled mechano-diffusion problems

In this manuscript, a new multiscale-multiphysics computational methodology is devised for analy-sis of coupled diffusion-deformation problems. The proposed methodology is based on the variational multiscale principles. The basic premise of the approach is accurate fine-scale representation at a small subdomain where it is known a-priori that important physical phenomena are likely to occur. The re-sponse within the remainder of the problem domain is idealized based on coarse-scale representation. We apply this idea to evaluate a coupled mechano-diffusion problem that idealizes the response of ti-tanium structures subjected to thermo-chemo-mechanical environment. The proposed methodology is employed to devise a multiscale model, in which the transport of oxygen into titanium is modeled as a diffusion process, whereas the mechanical response is idealized using concentration dependent elastic-ity equations. A coupled solution strategy based on operator split is formulated to evaluate the coupled multiphysics and multiscale problem. Numerical experiments are conducted to assess the accuracy and computational performance of the proposed methodology. Numerical simulations indicate that the variational multiscale enrichment has reasonable accuracy and computationally efficient in modeling the coupled mechano-diffusion response