International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

## Simulation of the dynamic contact interaction of elastic-plastic bodies using high-performance computing

The algorithm for numerical realization of boundary conditions of contact interaction of deformable bodies with beforehand unknown, time-dependent zone of contact is worked out. Contact conditions are formulated in the form of quasivariational inequality with one-sided constraint. This constraint corresponds to the condition of nonpenetration of deformable bodies into each other. Discrete inequalities are solved numerically in boundary meshes of the finite-difference grid by means of the method of successive approximations, on each step of which the projections of velocity vectors and some auxiliary vectors, serving for taking into account a friction in the contact zone, onto convex and closed sets of special form are constructed.
Dynamic deformation of elastic-plastic materials is described by the mathematical model taking into account small strains and finite rotations. This model consists of the system of equations of motion, the Hooke law for elastic constituents of the strain tensor, the equation for the rotation angle and the variational inequality of the principle of maximum of the energy dissipation power describing the process of plastic flow. The transition of material from elastic state to plastic one is determined by the Mises yield condition.
Parallel shock-capturing algorithm is proposed for implementation of this model on multiprocessor computer systems. It is based on the combination of splitting methods with respect to physical processes and spatial variables. The data exchange between processors occurs at step “predictor” of the finite-difference scheme with the help of shadow edges. Computation of the whole contact boundary is produced by a separate processor. To improve the approximation of geometrical constraints in the contact zone, the correspondence between boundary meshes of independent grids of interacting bodies is established and quasivariational inequality is solved on a grid refinement, common for two contacting surfaces.
Numerical computations for the problem of an oblique impact of two deformable plates in two-dimensional formulation were performed on cluster.

This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00053), by Complex Fundamental Research Program no. 2 of the Presidium of RAS (Intelligent Information Technologies, Mathematical Modeling, System Analysis and Automation) and by the Interdisciplinary Integration Project no. 40 of the Siberian Branch of RAS.