A dual approach in fracture mechanics based on complementary energy is proposed. 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 discontinuties. This energy release rate is given as a integral based on free or complementary energy. The invariance of integrals is analysed and the obtained results in elastoplasticity are discussed. The energy release rate is determined in terms of potential energy or complementary energy, first in elasticity and secondly in elastoplasticity. Associated to these definitions, the laws of propagation of the crack is chosen as a Griffith law and the propagation is governed by a normality rule. In this framework we formulate the evolution problem concerning crack propagation in an elastoplastic material. Variational formulations are obtained in terms of rate of displacement, of stresses and of crack length.