ONE-DIMENSIONAL CYLINDRICAL SHOCK WAVES UNDER CONDITIONS OF STRESS CAUSING A VISCOPLASTIC FLOW
In the framework of the theory of finite deformations, the features of modeling the response of an incompressible elastoviscoplastic cylindrical layer with preliminary antiplane deformations to essentially nonstationary boundary effects are considered. The formulation of the problem admits the existence and propagation of divergent shock waves with nonzero curvature, therefore, the representation of the solution behind the moving surfaces of strong discontinuities occurs by means of the nonlinear ray method. The preliminary state of the layer, determined by the solution of the static problem, is chosen in such a way that the shock loading moment coincide with the onset of the plastic flow on the inner surface of the layer. In this case, the boundary of the flow region is the shock wave of the load, and the next shock wave of circular polarization will propagate along the region containing irreversible deformations, which allows obtaining analytical expressions for an approximate solution.