In Fracture Mechanics, we are concerned with a continuum solid containing a crack. The medium is subjected to loadings applied externally at the surface. The evolution of the system with time is seek. In thermodynamics equilibrium, the system is characterized by its energy U that is function of various parameters such as crack-front spatial and angular coordinates, crack-length, crack-front speed, applied loadings, elastic constants and temperature T. U depends implicitly on time t trough the dependence on time of its various parameters. U is written as.