A general theory is developed for predicting stress and force histories for normal impact and penetration of geological targets by conical-nosed projectiles. To account for general material properties, the target medium is described by arbitrary hydrostat and shear failure-pressure relations. Using the cylindrical cavity approximation, the penetration dynamics reduce to a problem of radially symmetric stress wave propagation involving a nonlinear, ordinary, differential equation in terms of similarity variables. This equation is solved numerically by a shooting technique which is initiated by asymptotic values at the wave front. Numerical results are given for the stresses on the penetrator nose for some specific material models.

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