Rayleigh–Taylor instability in elastic-plastic solids

The linear analysis of incompressible Rayleigh–Taylor instability is carried out for thick solid plates accelerated uniformly by a constant pressure. The instability threshold is found and the boundary for the elastic to plastic transition is also determined. It is demonstrated that transition from the elastic to the plastic regime is a necessary condition for the onset of instability but not a sufficient one. The theory is in excellent quantitative agreement with the results of two-dimensional numerical simulations and reveals the main physical mechanisms that control the instability.