Nonlinear Deformation of Three-Dimensional Piecewise Homogeneous Media in Stress Waves

Abstract

The integral representation of the relevant boundary problems together with the difference approximation schemes of the time solution is used to simulate the nonlinear wave dynamics of threedimensional heterogeneous deformable media. The time solution of the integral equations is based on the Kelvin—Somigliana fundamental solution, the Newmark -scheme, the collocation approximation, and the predictor-corrector of the method of the theory of elastoplastic media flow with anisotropic hardening. The parametrization of the domain surface occupied by the medium, i.e., its internal boundaries, is made using the quadratic boundary elements. Similar volume elements are used to calculate the integrals with the bulk (inertial and viscous) forces and determine the plastic deformation zones. The complex histories of the combined shock loading of the composite piecewise homogeneous media slowly changing in time in the presence of the local zones of singular perturbation of the solution are considered. The discrete domain method was developed, based on which the practice-relevant nonlinear problems of stress wave propagation in heterogeneous media with the concentrators were solved.