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A method is developed for the numerical solution of dynamic elastic-visco-plasticity equations for isotropic and anisotropic cases. Anisotropic elastic-visco-plastic systems of equations often describe models of deformable solid media with a discrete set of slip planes (in layered and block media) with nonlinear slip conditions at contact boundaries. For a stable numerical solution of such systems of differential equations, an explicitly implicit method is proposed. An explicit approximation is used for the equations of motion while an implicit approximation is applied to the constitutive relations containing a small parameter in the denominator of the free term. Examples of numerical solutions are presented for dynamic problems on the reflection of waves from obstacles in the inelastic layered and block media with the formation of slip and delamination zones at the boundaries of structural elements.

Explicit-Implicit schemes for solving the problems of the dynamics of isotropic and anisotropic elastoviscoplastic media