Mathematical model for the numerical solution of nonstationary problems in solid mechanics by a modified Godunov method

A mathematical model of substance behavior under developed elastoplastic strains is worked out for solving one-dimensional problems of solid mechanics. The model is based on the fundamental laws of conservation of mass, momentum, and total energy, Wilkins model, kinetic model of substance destruction, and modified Godunov method for the numerical solution of problems in mathematical physics. A hybrid difference scheme is constructed, which approximates acoustics equations with constant coefficients in smooth flows for the case of plane symmetry with the second order in time and space.