Moving singularities in thermoelastic solids (original) (raw)

The solution of the evolution problem of a discontinuity requires the formulation of a kinetic law of the progress relating the driving force and the velocity of the singularity. In the case of a crack, the energy-release rate can be computed (in quasi-statics and in the absence of thermal and intrinsic dissipations) by means of the celebrated Jintegral of fracture that is known to be path-independent and, therefore, provides a very convenient estimation of the driving force once the field solution is known. However, the velocity at the crack tip remains undetermined. A similar situation holds for a displacive phase-transition front propagation. The driving force acting on the phase boundary can be determined, but not the velocity of the displacive phasetransition front.