Introduction to the thermomechanics of configurational forces

Abstract

Configurational forces are thermodynamic conjugates to irreversible material body evolutions such as extension of cracks, progress of phase-transition fronts, movement of shock waves, etc. They do correspond to a change of material configuration. Accordingly, their realm is the material manifold of a body. Furthermore, they acquire a physical meaning only in so far as they contribute to the global dissipation. Therefore, the present contribution of a pedagogical nature proposes a primer introduction to the thermodynamics of configurational forces. To that purpose, we first introduce a consistent thermomechanics of general deformable continua on the material manifold (and not in physical space). This is achieved in a canonical manner by full projection of the balance equation of momentum onto the material manifold and constructing in parallel a formally consistent expression of the energy conservation. Then various configurational forces such as those appearing in inhomogeneous bodies, at the tip of a propagating crack, at the surface of a propagating phase-transition front, or of a shock wave, and those due to local structural rearrangements (plasticity, damage, growth), are examined from the point of view of their dissipated power.