We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.
Roubicek, T., Tomassetti, G. (2015). Thermomechanics of damageable materials under diffusion: modelling and analysis. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 66, 3535-3572 [10.1007/s00033-015-0566-2].