Thermomechanics of forces driving singular point sets

Abstract

By treating in parallel the balance of canonical momentum and the entropy equation, both at regular material points and at singular sets such as discontinuity fronts, it is shown that a consistent thermomechanics of such fronts can be constructed, especially with regard to shock waves and phase-transition fronts. Within this framework, two extreme singular cases are that of the classical shock-wave theory which relates dissipatively two states in adiabatic evolution, and that of the nondissipative phase transition which relates two generally dissipative states. In both cases, the driving force on the singular set is made to vanish yielding oversimplifications. This is obviously corrected by showing that if dissipation occurs at all, such a driving force should not be zero. It is in fact related to the details of what happens within a structured front and to the noninertial motion of such a front viewed as a quasi-particle. In passing, the role of a generating (thermodynamic) function for discontinuity fronts is exhibited.