An approximate formulation of the problem of dynamic plastic instability in a thin sheet of material subjected primarily to enertial forces is presented. It is shown that the classic static plastic instability condition reappears with a new and more detailed interpretation. When perturbations are introduced at strain values less than the critical strain, they tend to smooth out in a calculable and rapid rate. When similar perturbations are introduced or remain after the critical strain level is passed, they develop in a calculable way at a progressively accelerated rate. The details depend strongly on whether or not perturbations are themselves work hardened. The size of a “critical flaw” is related to the strain rate, with the consequence that the definition of “quasi-static” conditions in the context of the present theory becomes self-evident. The net distortion of the perturbation depends strongly on the rate of expansion of the plate and the size of the perturbation in ways that are shown by analytical and numerical solutions of the equations.

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