A closed-form assessment of residual cavity depth ('damage') left after a rigid object (spherical or rod-like 'foreign object') impacts a rigid-plastic target is suggested. The formulation of such dynamic process is based on the dynamic upper bound to Mises-type materials impacted by projectiles of known kinetic energy (mass and impact speed). It enables to account for the inertial force of the projectiles which drives the penetration. Distinction is made between the behavior of brittle-like and ductile-like targets by viewing the post-penetration morphology with either falling-off or piling-up of the removed material, respectively. The solution assesses explicitly the resistance of the targets to penetration at any prescribed interfacial friction. It also assesses rigorously the residual depth of the impacted objects without reliance otherwise on heavy numerical methods (though FE solution by ABAQUS code provides a favorable numerical check).
Comparisons to experiments are satisfactory. They are based on shooting Maraging-steel rods with spherical front face into aluminum targets at moderate speeds (at most 1000 m/ s). When one replaces the empirically-oriented matched parameters of Poncelet's formula by the suggested upper-bound theoretical-based parameters, the agreement with experiments seems excellent compared to other alternatives.