  A mathematical model for an elastoplastic porous continuum subject to large
strains in combination with reversible damage (aging), evolving porosity, 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 flash
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. Existence
of suitably defined weak solutions and a convergence result for Galerkin
approximations is proved.
