Progress of phase boundaries and walls in thermo-deformable solids : A canonical approach

Four approaches at different scales or levels of understanding are proposed to study the propagation of phase boundaries and domain walls in thermo-deformable solids : (i) a microscopic one relying on a lattice model that yields the representation of the thin transition zone as a solitonic structure ; (ii) a thermodynamic macroscopic one that is based on the use of jump relations associated with the canonical formulation of continuum mechanics on the material manifold, (iii) a mesoscopic continuum approach using directly a mixed viscosity-strain-gradient modelling, and (iv) a global quasi-particle viewpoint which, although accounting for the structure of the transition zones, is also canonical and allows for the study of transient motions of these zones. The common points and respective interests of the approaches are discussed