Duality in process of noncommutative deformation and topological nature of Cherepanov-Rice integral

Abstract

In t his paper it is showed, that for the noncommutative deformation simultaneously there exist also loading deformation H, and unloading deformation \(H^v\). The real deformation is a combination of these types of deformations. The criterion of destruction J reflects topological character of medium, i.e. it defines properties of symmetry of medium at destruction. It is possible to tell, that during destruction the energy is released not continuously but and discretely. This situation is reflected through topological number Q or number of unloading, connected to him.