Formulas for calculating the depth of penetration of projectiles of different shapes into anisotropic barriers

We consider the high-speed penetration of impactors with similar cross sections (pyramids, not necessarily regular, bodies of revolution, thin bodies with an arbitrary shape of the cross section) into barriers with a dynamic hardness that continuously changes depending on the depth of the shield. The description of the interaction of the barrier with the impactor is based on the Vitman-Stepanov model; the effects associated with incomplete immersion of the impactor in the barrier at the initial stage are not taken into account. Explicit formulas describing the dependence of the penetration depth on the impact velocity, the shape of the impactor, and the mechanical properties of the barrier material are obtained.