Thermodynamics of elastoplastic porous rocks at large strains towards earthquake modeling

A mathematical model for an elastoplastic porous continuum subject to large strains in combination with reversible damage (aging), evolving porosity, and water and heat transfer is advanced. The inelastic response is modeled within the frame of plasticity for nonsimple materials. Water and heat diffuse through the continuum by a generalized Fick-Darcy law in the context of viscous Cahn{Hilliard dynamics and by Fourier law, respectively. This coupling of phenomena is paramount to the description of lithospheric faults, which experience ruptures (tectonic earthquakes) originating seismic waves and ash heating. In this regard, we combine in a thermodynamic consistent way the assumptions of having a small Green{Lagrange elastic strain and nearly isochoric plastification with the very large displacements generated by fault shearing. The model is amenable to a rigorous mathematical analysis. The existence of suitably defined weak solutions and a convergence result for Galerkin approximations is proved.