Dual integrals in non linear fracture mechanics

The purpose of this paper is to propose a dual approach in fracture mechanics based on complementary energy. The analysis of the dissipation shows that the thermodynamical force associated with the evolution of a crack is an energy release rate, form of which depends on the presence or not of mechanical discontinuities. This energy release rate is given as an integral based on free or complementary energy. The invariance of such integrals is analysed and the obtained results in elastoplasticity are discussed. The energy release rate is analysed in terms of potential energy or complementary energy, in linearized elasticity and in elastoplasticity. Associated to these definitions, a law of crack propagation is chosen as a Griffith law and the propagation of a crack is studied.