THE DYNAMICS OF CONFIGURATIONAL FORCES AT PHASE-TRANSITION FRONTS

First we recognize that the coherence of certain phase transformations in solids is most vividly expressed using the material manifold and within the kinematic continuum description based on the so-called inverse motion. In this fully dynamical framework the equation of interest is the un-balance of pseudomomentum for thermoelastic conductors. On computing the power developed by the accompanying surface source of quasi-inhomogeneities at the phase-transition front, we show that this relates directly to the normal jump of the Eshelby stress - devoid of any kinetic energy, but computed from the free energy - a scalar quantity which may be referred to as the Hugoniot-Gibbs configurational force at the front. The thermodynamic analysis also establishes that this power is dissipated as the material progresses at the front that is homothermal. The jump relation including this dissipation is that associated with the heat propagation equation valid at regular points. In all, this approach is based on the theory of material uniformity and inhomogeneities as developed in recent years by M. Epstein and the authors. All reasonings are made in full dynamics, for finite strains, and any anisotropy in three dimensions.