Simulation of nonlinear deformation and fracture of heterogeneous media based on the generalized method of integral representations

Development of BIEM (boundary integral equation method) for solving of nonlinear 3D problems of thermal elastic-plastic deformation and fracture of heterogeneous complex shapes bodies with changing boundary conditions in the process of loading is proposed. Collocation approximation to the solution of equations is based on the fundamental solution of the Kelvin–Somalian and flow theory of elastoplastic media with anisotropic hardening. The cases of complex, composite thermo-mechanical loading of piecewise homogeneous media, including in the presence of local zones of singular perturbation solutions — randomly oriented defects such as cracks are considered. Solutions for practical importance of 3D nonlinear problems are obtained using a previously developed method of discrete domains (DDBIEM).