A note on crack propagation paths inside elastic bodies

The note is concerned with a model of linear elastostatics for a two-dimensional inhomogeneous anisotropic body weakened by a single straight crack. On the crack faces, nonpenetration conditions/Signorini conditions are imposed. Relying upon a higher regularity result in Besov spaces for the displacement field in a neighborhood of the crack tip, we prove that the energy release rate is actually independent of the choice of a subsequent crack path (among the possible continuations of class H³).