Duality and symmetry lost in solid mechanics

Some conservation laws in Solids and Fracture Mechanics present a lack of symmetry between kinematic and dynamic variables. It is shown that Duality is the fight tool to re-establish the symmetry between equations and variables and to provide conservation laws of the pure divergence type which provide true path independent integrals. 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.