Two-dimensional thermo-viscoelastic waves in layered media

Abstract

Dynamic problems of deformation of solids have been the subject of numerous studies in the CIS and abroad. The rejection of a number of simplifying assumptions made in the cited and other published works leads to the need for further refinement and improvement of mechanical and mathematical models describing the kinematics and stress state of both the drummer and the barrier. Further, the axisymmetric collision of a cylindrical indenter with an obstacle in the form of a package of isotropic plates containing free cavities and rigid inclusions is numerically investigated within the framework of the coupled theory of thermoviscoelasticity. Various formulations of the problems of the theory of elasticity and thermo-viscoelasticity are possible. However, the used formulation in velocities and stresses is one of the most universal, since it allows solving the main boundary value problems (including mixed ones) by a uniform way. The paper gives a grid-characteristic scheme and its convergence. In accordance with the theory of A.A. Samarskii, the stability in the energy norm of the grid problem is proved.