RAYLEIGH-TAYLOR STABILITY-CRITERIA FOR ELASTIC-PLASTIC SOLID PLATES AND SHELLS

The Rayleigh-Taylor (R-T) instability theory is usually applied to the acceleration of one fluid by a lower density one, but also becomes ap plicable to a solid accelerated by a fluid at very high pressure. Appr oximate analytic R-T stability criteria are derived for both finite an d infinitesimal perturbations of the driven surface of an incompressib le solid plate of a given thickness, shear modulus, and von Mises yiel d stress uniformly accelerated by a massless fluid. The Prandtl-Reuss equations of elastic-plastic how are assumed for the solid. A single d egree of freedom, amplitude q, is assumed for the spatial dependence o f the perturbation, which is approximated to be that of the semi-infin ite half-plane ideal fluid linear R-T eigenfunction. The temporal depe ndence of q, however, is determined self-consistently from global ener gy balance, following a previously published model. The (significant) effect of the unperturbed solid's stress tensor is included and relate d to the converging/diverging geometries of imploding/exploding cylind rical and spherical solid shells for which the model may be applied lo cally. Correlations with Phillips Laboratory's quasi-spherical electro magnetic implosions of solid shells are presented. (C) 1997 American I nstitute of Physics.