THE METHOD OF DECOMPOSITION OF GAPES IN THE THREE-DIMENSIONAL DYNAMICS OF ELASTOPLASTIC MEDIA

A numerical method for calculating the three-dimensional processes of impact interaction of elastoplastic bodies with large displacements and deformations based on the method of disintegration of discontinuities according to the Godunov scheme is presented. To integrate the equations of dynamics of an elastoplastic medium, the principle of splitting in space and in physical processes is used. The Riemann's solver for an elastic medium in the case of an arbitrary stress state are obtained and presented. A modification of the scheme is described that allows one to obtain solutions in smoothness domains with a second order of accuracy on a compact template for moving Eulerian – Lagrangian grids. Three types of difference grids are used. The first – a moving surface grid – consists of a continuous set of triangles that limit and accompany the movement of bodies; the size and number of triangles in the process of deformation and movement of the body can vary. The second – a regular fixed Eulerian grid – is limited to a surface grid; separately built for each body; integration of equations takes place on this grid; the number of cells in this grid can change as the body moves. The third grid is a set of local Eulerian – Lagrangian grids attached to each moving triangle of the surface from the side of the bodies and allowing to determine the parameters on the boundary and contact surfaces. The values of the underdetermined parameters near the contact boundaries on all types of grids are interpolated. Comparison of the obtained solutions with the known solutions and with the experimental data, shows the efficiency and sufficient accuracy of the presented three-dimensional methodology.