On the universality of the thermomechanics of forces driving singular sets

Summary It is shown that the formal expression of the driving force acting on a one- dimensional or two-dimensional singular set of material points (crack tip in fracture, phase-transition front or shock wave) and of the accompanying dissipation in an irreversible progress of the set is independent of the precise material behaviour at regular points. A four-dimensional space-time canonical formalism is introduced establishing the necessary consistency between the power expended by the driving force (spatial component) and the resulting heat source (timelike component) localized at the singular set. Possible extensions of this result are discussed. Received 8 April 1999; accepted for publication 4 May 1999