Shock-Wave Propagation in Solid and Compactible Media

Abstract

The equations of motion for a hydrodynamic solid are studied for a pressure-density relation appropriate to pulse propagation in solid and compactible media. After collapse of the compactible material, the pressure-density relation is assumed to have the form P = A[(ρ/ρ0)γ−1]. A semianalytical method of solution is used on the resulting one-dimensional set of nonlinear partial differential equations. By using characteristic variables, the nonlinear differential equations are transformed to a set of linear partial differential equations whose solution is then obtained numerically. Applications are made to aluminum, for which the constants A and γ are known, and to compactible materials using an assumed value for γ. This investigation serves to define the various types of phenomena that can occur in a semi-infinite compactible material that is shocked by a rectangular pressure pulse. In particular, the analysis shows that the shock-wave penetration depth at the end of the first shock-rarefaction interaction has a minimum when regarded as a function of the material porosity.