Boundary Integral Equation Method in the Modeling of Nonlinear Deformation and Failure of the 3D Inhomogeneous Media

The method of boundary integral equations is applied for solving the nonlinear problems of thermo-elastic-plastic deformation and fracture of inhomogeneous 3D bodies of the complex form. Solution is constructed on the basis of the generalized identity of Somigliana involving method of sequential linearization in the form of initial plastic deformations. The increments of plastic deformation are determined on the basis of the flow theory of hardening elastoplastic media with the use of modifed Prandtl–Reus's relations. The cases of complex thermo mechanical loading of compound piecewise homogeneous media in contact are considered. For describing the processes of nonlinear deformation and fracture of the bodies with a complex geometry and local peculiarities a method of discrete domains (DDBIEM) is developed. The solutions of some practical significant 3D non-linear problems of the mechanics of deformation and fracture are presented.