Processes of self-organisation of stable structures in physical systems of different nature are one of important demonstrations of non-linear science. Processes of self-organisation of adiabatic shift zones in materials under deformations are the example of such processes. For the past decade this phenomenon has attracted a lot of attention and is intensively studied by a group of Department № 31 “Applied mathematics” employees under the supervision of Prof. N.A. Kudriashov, because it turned out that adiabatic shift zones are one of main physics of failures of a series of technologically important materials, subjected to shear deformations. Places of localisation of adiabatic shift zones are more fragile than surrounding areas, that’s why destruction of materials in the field of localization of shift zones takes place under destruction. This phenomenon was observed in technologically important processes of manufacturing, nuclear, and space industries, and in many physical experiments. The examples of such processes can be found in the work of nuclear reactor, in launch and destruction of space vehicles, in material rupture at high speed, in material processing by pressure, in mechanical material processing, under pressing etc., which determines scientific relevance and importance of conducted research.

Adiabatic shift zone is an area with the width from 1 to 500 μm, in which of time high temperatures and deformations are achieved for a short period. Usually processes of forming of adiabatic shift zones are formed in places of defects’ presence, and these could be structural or geometric defects, as well as thermal ones. It has been ascertained in a series of experimental works that processes of self-organisation of adiabatic shift zones take place at high initial speeds of deformation. However, in spite of high practical value of this phenomenon, it is still understudied.

The phenomenon of adiabatic shift zones’ formation is mainly studied, using experimental approach. Such approach to the research of physical processes is effective, but more resource-intensive and time-consuming. In connection with it studying of processes of adiabatic shift zones’ formation is made with the help of calculation experiments, which allow research all the peculiarities of the processes from the initial stage to the final one.

Apart from experimental works, the processes of adiabatic shift zones’ formation are intensively studied using theoretical methods. However, currently, there are no works on research of processes of self-organisation of adiabatic shift zones. Hence this phenomenon is understudied, which determines significant scientific novelty of the research, conducted at Department № 31.