Steady, Structured Shock Waves. Part 1: Thermoelastic Materials

Abstract

One dimensional plane shock waves have been widely used to study the mechanical response of solids to high velocity impact★. For many materials, under a certain range of impact pressures, a two-wave structure arises, the first wave of which, the so-called elastic precursor, travels at a velocity near to the speed of sound, while the second wave, often called a plastic shock wave, travels at a slower speed which increases with impact pressure. While the full two-wave structure is thus not steady (does not propagate without change of form), each component wave may be treated as steady after having propagated sufficiently far.† As indicated by the experimental data presented in Figure 1, in some materials the elastic precursor is generally much steeper than the plastic shock wave. Indeed, for some materials, the elastic precursor is infinitely steep to within current techniques of data resolution. Accordingly, it is usually modelled as a singular surface. The plastic shock, however, typically exhibits a smooth variation, albeit still highly localized in time and space. Thus, these shocks are structured, and a central question for constitutive modelling concerns those aspects of material response that can serve as structuring agencies in the shock‡.