This paper concerns the mathematical modelling of high rate penetration of a metaltarget by a shaped charge device that produces a high velocity jet. A key objective is to predict the penetration velocity, be it subsonic, transonic, or supersonic. We do this by considering, on the local scale near the tip of the penetrated cavity, an elastic-plastic free boundary problem that takes into account the residual stresses produced by the moving plasticized region of the target. It is the self-consistency of this elastic-plastic model that dictates predictions for the penetration velocity
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