Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration

Abstract

A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.

Analytic model for the dynamic Z-pinch

“…9 Finally, the model may have the potential to be generalized in many different directions, depending on the particular application, without breaking the simplifying approximation regarding the identification of the piston acceleration with the mass averaged acceleration of the shocked materialnamely, arbitrary shock intensity, ionization effects, twodimensional geometry. …”