Impact a circular cylinder with a flat on an elastic layer

Abstract

In the work the comparison of the results of solving two plane problems is performed: the impact of a circular cylinder with a plane platform parallel to the cylinder axle (the flat) with an elastic layer and a second − plane strain state of nonstationary interaction of a circular cylinder with a flat with an elastic layer in a purely elastic and elastic-plastic mathematical formulation corresponding. The first contact occurs along the plane of the flat. A good coincidence of the results of the second problem at an elastic stage with the results of the first problem is shown. In the author's works a new approach was developed to solve plane and tree dimension problems of impact and non-stationary interaction in an elastoplastic formulation. The crack growing was simulated using an elastoplastic mathematical model. The numerical solution was obtained using the finite difference method scheme.The use of an elastic-plastic formulation makes it possible: 1) determine the stress-strain state at the points determined by the partitioning grid of the computational domain, not only on the surface; 2) to give a reliable description of the development of plastic deformations − the stage corresponding to plasticity is a continuation of the elastic stage; 3) reliably determine the destruction toughness. A method has been developed for calculating plastic strain fields and destruction toughness of the material using the solutions of dynamic plane problems of the stress-strain state in an elastoplastic formulation taking into account possible material unloading; 4) to verify and calibrate the solution of problems in an elastoplastic formulation for the first steps by time when the deformation process is elastic, it is convenient to use the solution of the corresponding elastic problem.