Abstract
In this chapter, we consider the dynamic loading problem of a deformable solid medium containing slip planes with nonlinear slip conditions on compressed contact boundaries and weak delamination on stretched ones. The explicit–implicit scheme is constructed for the numerical solution of the governing system of equations, which is exactly reduced to adjusting the values of the stress tensor after performing an elastic step. The elastic step is calculated using an explicit grid-characteristic method. The implicit approximation of the constitutive relations containing a small parameter in the denominator of nonlinear free terms is performed with the second approximation order and is consistent with the explicit elastic step. The correction procedure is also applicable for those cases when the viscosity parameter of interlayers providing the sliding mode of contact boundaries is not small. In the stretched mode, equations of an effective transversely isotropic elastic medium are obtained. They are also solved by the grid-characteristic method with a consistent approximation order. The solution of the seismic wave propagation problem in an inhomogeneous fractured geological massif is obtained numerically in a two-dimensional formulation.
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This work was supported by the Russian Science Foundation, grant no. 19-71-10060.
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Nikitin, I.S., Golubev, V.I. (2022). Higher Order Schemes for Problems of Dynamics of Layered Media with Nonlinear Contact Conditions. In: Favorskaya, M.N., Nikitin, I.S., Severina, N.S. (eds) Advances in Theory and Practice of Computational Mechanics. Smart Innovation, Systems and Technologies, vol 274. Springer, Singapore. https://doi.org/10.1007/978-981-16-8926-0_19
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DOI: https://doi.org/10.1007/978-981-16-8926-0_19
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