Impact of rigid body and viscous-plastic rod of finite length

The impact of a rigid body and rod finite length made viscoplastic incompressible material moving towards each other at constant velocity is studied in the article. One-dimensional motion considered, i.e., velocity, stress, parameters are considered to be averaged over section. According model viscous-plastic material, divided into two parts: region plastic strain that moves as solid after impact. boundary between these regions unknown needs determined. As result, we arrive problem with free boundary, well-known example which Stefan problem. However, formulation under consideration differs significantly from In addition, function determined describes contrast problem, not explicitly present conditions. There various numerical methods for solving problems an boundary. known, implementing associated significant difficulties. this article, method integral relations used - modification Karman-Pohlhausen known layer theory. reduced Cauchy system nonlinear ordinary differential equations proposed solved by successive approximations Runge-Kutta method. Numerical calculations were performed. influence changes mass magnitude velocities on size change stresses contact surface revealed.