Spherically Symmetric Shock Waves in Materials with a Nonlinear Stress-Strain Dependence

Abstract

The paper considers the dynamic deformation features of constructional materials with nonlinear stress-strain dependence. For the one-dimensional shock waves with nonzero curvature arising in constructions under dynamic loading the propagation regularities are studied on the basis of the matched asymptotic expansions method. In the nonstationary problem with the longitudinal spherical shock wave the relations for simultaneous consideration of dynamic properties in the outer and inner problem of the perturbation method are obtained. The solution in the front-line area is constructed on the basis of the evolution equation different from ones for a plane longitudinal wave. The need for a solving of an additional ODE system for matching outer and inner expansions is shown. It is obtained that the outer solution asymptotics in the spherically symmetric problem contains waves reflected from the leading front in contrast to the solution behavior behind the front of the plane shock wave.