ABSTRACT
To this scope, we start with the global balance laws as it is used to do in any other problem in continuum mechanics. More specifically, we consider an elastic body with a propagating crack in its interior and postulate the balances for all relevant fields, included the configurational ones, for any arbitrary part of the body (Agiasofitou and Kalpakides 2003). In the presence of the crack, this procedure becomes much more complicated because of two reasons. Firstly, the involved fields are not continuous across the crack, even more, they may have a singularity at the crack tip and second, the underlying kinematics is more complicated due to the presence of the separate crack kinematics. In particular, the singularities at the crack tip make necessary to reformulate the transport and divergence theorems, which are indispensable for any localization process.
