Rayleigh–Taylor stability criteria for elastic-plastic solid plates and shells

Abstract

The Rayleigh–Taylor (R-T) instability theory is usually applied to the acceleration of one fluid by a lower density one, but also becomes applicable to a solid accelerated by a fluid at very high pressure. Approximate analytic R-T stability criteria are derived for both finite and infinitesimal perturbations of the driven surface of an incompressible solid plate of a given thickness, shear modulus, and von Mises yield stress uniformly accelerated by a massless fluid. The Prandtl-Reuss equations of elastic-plastic flow are assumed for the solid. A single degree of freedom, amplitude $q$ , is assumed for the spatial dependence of the perturbation, which is approximated to be that of the semi-infinite half-plane ideal fluid linear R-T eigenfunction. The temporal dependence of $q$ , however, is determined self-consistently from global energy balance, following a previously published model. The (significant) effect of the unperturbed solid’s stress tensor is included and related to the converging/diverging geometries of imploding/exploding cylindrical and spherical solid shells for which the model may be applied locally. Correlations with Phillips Laboratory’s quasispherical electromagetic implosions of solid shells are presented.