Conservation laws, duality and symmetry loss in solid mechanics

The paper deals with conservation laws which are not of the pure divergence type and thus do not provide a path-independent integral for use in Fracture Mechanics. It is shown that Duality is the right tool to re-establish the symmetry between equations and to provide conservation laws of the pure divergence type. The loss of symmetry of some energetic expressions is exploited to derive a new method for solving some inverse problems. In particular, the earthquake inverse problem is solved analytically