Multidomain mixed variational analysis of transport flow through elastoviscoplastic porous media

Multidomain mixed nonlinear transport and flow phenomena through elastoviscoplastic porous media is variationally analyzed. Mixed variational formulations of the poro-mechanical system are established via composition duality methods, determining solvability results on the basis of duality principles. The conformation of the coupled physical system corresponds to constrained transport processes driven by a compressible Darcian flow, in a quasistatic elastoviscoplastic deformable subsurface porous media, modeled variationally by primal evolution mixed transport and consolidation, and dual evolution mixed flow and quasistatic deformation. For parallel computing, non-overlapping multidomain decomposition methods based on variational macro-hybridization, are presented and discussed, providing a natural multi-physics approach for the coupled transport flow and deformation system. For computational realizations, internal variational macro-hybrid mixed semi-discrete approximations are given, as well as primal and dual fully discrete semi-implicit time marching schemes. Furthermore, the corresponding coupled transport-flow-deformation system is concluded and analyzed, proposing natural resolution coupling techniques.