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

TL;DR

This paper explores the duality of loading and unloading deformations in noncommutative deformation processes, linking the destruction criterion to topological properties and energy release patterns.

Contribution

It introduces a novel perspective on noncommutative deformation by connecting topological invariants to the destruction process and energy release behavior.

Findings

Existence of simultaneous loading and unloading deformations

Destruction criterion reflects environmental symmetry

Energy release occurs discretely during destruction

Abstract

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