Phenomenological derivation of the thermomechanical diffuse-interface model for electric breakdown

In this work we derive diffuse-interface type model for electric breakdown evolution in solid dielectrics which accounts for non-isothermal and mechanical effects. The proposed model consists of mass, momentum and energy conservation equation, Maxwell’s equations in quasi(electro)static approximation and Allen-Cahn type equation which describes phase-field evolution. The derivation of the model is based on the rational thermomechanics framework, M. Gurtin’s microforce and microstress theory and Coleman-Noll procedure.