Shock Waves in Continuous Elastic Media

An amazing feature of shock compression is illustrated in Figs. Id-e. A driven shock front steepens up as it runs, in contrast to acoustic waves that disperse as they run [1]. Imagine a shock front that is not initially steep (Fig. Id). Think of the front as a higher pressure wave trailing a lower pressure wave. Equation (2) above shows the trailing wave moves faster. In an ideal continuous elastic medium, the shock front steepens until it becomes an abrupt discontinuity. The shock front risetime tr — 0. 

Shock compression is an irreversible adiabatic compression that heats the material behind the front [1]. The temperature rise can be divided into two parts. The minimum temperature rise would result if shock compression were slow enough that it approximated a reversible adiabatic compression from Vq to Vj. This process, where zlS = 0, is also called an isentropic compression [1]. Due to the irreversible nature of shock compression, an additional rise is produced that results from the entropy increase zl5,vr across the shock front. This additional rise depends on the detailed nature of the shock front. Shock compression is hotter than isentropic compression. The new temperature Tj cannot be determined from the Hugoniot-Rankine equations alone. Some kind of equation of state (EOS) is also needed (for state-of-the art examples see Refs. [12-14]), and the usual choice is a Griineisen equation of state. The temperature Ti is given by [1], 

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