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

Abstract

A mathematical model of micro-plasticity is developed for the description of nonlinear, depending on the time and deformation rate behavior of polycrystalline material-metals with micro damages-initial and appearing in the process of shock waves propagation. It is a development of the Afanas’ev-Bessiling model, generalized on account of the viscosity and microinhomogeneity of the deformed media with the anisotropic work-hardening, hysteresis losses, and Bauschinger’s effect of shock influences. The microflaws in the media are examined as cavitational discontinuities (pores), diffused upward evenly in a microvolume. The so-called local models of damage mechanics are used for a description of their kinetics on the fronts of shock waves. The proposed model naturally and effectively makes it possible to study thin-walled shell constructions as a three-dimensional multilayered medium, with uniform or composition layers closely packed along the thickness. The solution of boundary value problems is built on the basis of difference schemes of approximation in space and time. The results of modeling nonlinear wave processes in a shell construction under the action of a local explosion are also presented.