The concept of a balance law for a cracked elastic body and the configurational force and moment at the crack tip

In this work, the derivation of the configurational equations for a cracked elastic body by postulating balance laws, is studied. To this end, a proper kinematics is proposed, according to which the evolution of the crack in the material configuration and the physical motion (deformation) are separated. A rigorous localization procedure provides the local equations in material space holding in the smooth part of the body, the corresponding jump conditions along the crack, as well as the configurational force and moment at the crack tip. The results are discussed in connection with the corresponding ones of fracture mechanics and some new interpretations are proposed.