solid dynamics, elastoviscoplasticity, shock waves, incompressibility, numerical methods, ray series

The one-dimensional problem of loading elastoviscoplastic cylindrical layer with preliminary deformations of a twisting type demonstrates the application of the method of ray series to obtain an approximate solution with two closely spaced discontinuity surfaces for example. This solution proves to be applicable in numerical calculations, which are conducted for the purpose of verification of the method relations and for the extension of the scope of its definition at times that are substantially longer than the use of only the ray method. Assumptions of smallness of reversible or irreversible deformation are not done, therefore the theory of large elastoplastic deformations is used, due to which the questions of the choice of the objective derivative and the separation of finite deformations into components.

Kovtaniuk Larisa Valentinovna, e-mail: lk@iacp.dvo.ru, Dr. Sci. Phys. & Math., Head of the Laboratory of Irreversible Deformation, Institute of Automation and Control Processes FEB RAS, Vladivostok, Russia.

Shtuka Victor Igorevich, e-mail: onslice@mail.ru, Post-Graduate Student, Mathematician Engineer, Institute of Automation and Control Processes FEB RAS, Vladivostok, Russia.