On the Convergence of Strong Cylindrical and Spherical Shock Waves in Solid Materials

Abstract

In this article, we present a description of the behaviour of shock-compressed solid materials following Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have employed it to investigate the propagation of cylindrically and spherically symmetric converging shock waves in solid materials. The analytical solution of shock dynamics equations has been obtained in the strong-shock limit, assuming the solid materials to be homogeneous and isotropic and obeying the Mie-Grüneisen equation of state. The non-dimensional expressions are obtained for the velocity of shock, the pressure, the mass density, the particle velocity, the temperature, the speed of sound, the adiabatic bulk modulus, and the change-in-entropy behind the strong converging shock front. The influences as a result of changes in (i) the propagation distance r from the axis or centre \((r=0)\) of convergence, (ii) the Grüneisen parameter, and (iii) the material parameter are explored on the shock velocity and the domain behind the converging shock-front. The results show that as the shock focuses at the axis or origin, the shock velocity, the pressure, the temperature, and the change-in-entropy increase in the shock-compressed titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc.