Transient dynamics of 3D inelastic heterogeneous media analysis by the boundary integral equation and the discrete domains methods

For the study of transients in 3D nonlinear deformable media we develope modeling methods which based on integral representations of 3D boundary value problem of elastic dynamics, numerical high-order approximation schemes of boundaries and collocation approximation of solutions. The generalized boundary integral equation method formulations using fundamental solutions of static elasticity, equation of state of elastoplastic media with anisotropic hardening and difference methods for time integration are represented. We take into account the complex history of combined slowly changing over time and impact loading of composite piecewise-homogeneous media in the presence of local perturbation solutions areas. With the use of this method and discrete domains method the solutions of applied problems of the propagation of non-linear stress waves in inhomogeneous media are received. Comparisons with the solutions obtained by the finite element method are represented also. They confirm the computational efficiency of the developed algorithms, as well as common and useful for practical purposes of the proposed approach.