Abstract
Continual models of solid media with a discrete set of slip planes (layered, block media) and with nonlinear viscous-plastic type slip conditions at the contact boundaries of structural elements are constructed. The resulting system of equations contains a small viscosity parameter in the denominator of nonlinear free terms. For a stable numerical solution of a system of differential equations, an explicit-implicit method is proposed with an explicit approximation of the equations of motion and an implicit approximation of the constitutive relations containing a small parameter. Examples of numerical solutions of dynamic problems on the scattering of waves on layered cluster in an elastic medium, on the formation of slip and delamination zones at the boundaries of structural elements are given.
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