Numerical simulation of high-speed dynamics of the nonlinear deformation and failure of damaged medium

For description nonlinear, depending on time and rate of loading behaviour of polycrystalline materials-metals with initial and appearing in the process of distribution of shock waves microdamages the mathematical model of microplasticity is developed. It is development of model of Afanas'ev–Bessiling, generalized on the account of viscosity and microinhomogeneity of the deformed media with the anisotropic work-hardening, hysteresis losses and Baushinger' effect at shock influences. Micro flaws in a media examined as cavitational discontinuities (pores), up-diffused evenly in a micro volume, for description of their kinetics on fronts of shock waves the so-called local models of damage mechanics are used. The proposed model naturally and effectively makes it possible to study thin-walled shell constructions as three-dimensional laminar medium with the uniform or composition layers close-packed along the thickness. The solution of boundary value problems is built on the basis of difference schemes of approximation on space and time. Results of modeling of nonlinear wave processes in a shell construction under action of local explosion also are presented.