Richtmyer-Meshkov instability in elastic-plastic media

An analytical model for the linear Richtmyer-Meshkov instability in solids under conditions of high-energy density is presented, in order to describe the evolution of small perturbations at the solid-vacuum interface. The model shows that plasticity determines the maximum perturbation amplitude and provides simple scaling laws for it as well as for the time when it is reached. After the maximum amplitude is reached, the interface remains oscillating with a period that is determined by the elastic shear modulus. Extensive two-dimensional simulations are presented that show excellent agreement with the analytical model. The results suggest the possibility to experimentally evaluate the yield strength of solids under dynamic conditions by using a Richtmyer-Meshkov-instability-based technique.

Figure 1

Diagram of the solid-vacuum interface and of the shock wave separating the shocked region from the material unaffected by the shock

Figure 2

Relative perturbation amplitude as a function of time for different values of the yield strength $Y$. Perturbation growth for an ideal fluid (classical) and for a pure elastic medium are also shown.

Figure 3

Relative perturbation amplitude as a function of time for a typical case. Amplitude and frequency vary during the first oscillation period of the elastic phase.

Figure 4

Comparison between the initial velocity ${\dot{\xi }}_0$ with the classical asymptotic value $k{\xi }_i{u}_p$. Dots are obtained from the numerical simulations.

Figure 5

Maximum relative amplitude as a function of the parameters combination $\rho {\dot{\xi }}_0^2∕kY$. Dots are obtained from the numerical simulations.

Figure 6

Relative time at which maximum amplitude is achieved as a function of the parameters combination $\rho {\xi }_0∕kY$. Dots correspond to the same cases as indicated in Fig. 5.

Figure 7

Oscillation period in the asymptotic elastic regime. Dots are obtained from the numerical simulations.

Figure 8

Relative mean value of the maximum amplitude ${\xi }_m-\overline{\xi }$ as a function of the parameters combination $Y∕kG$. Dots are the result of numerical simulations.