Mathematical modeling of the dynamics of layered and block media with nonlinear contact conditions on supercomputers

Abstract

Continual models of solid media with a discrete set of slip planes (layered, block media) and with nonlinear slip conditions at the contact boundaries of structural elements are constructed. The constitutive equations of the resulting system of equations contain 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. From implicit nonlinear difference approximations analytically, using the perturbation method, various effective formulas for the correction of stress components after an elastic time step are obtained. To calculate the elastic step, we used a grid-characteristic method on hexahedral grids, which allowed us to significantly increase the speed of calculations and simulate a non-stationary three-dimensional problem of generating a response from an oriented layered or block cracked cluster located in a homogeneous medium.