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We developed engineering models for forces on rigid, long rods with spherical, ogival, and conical noses that penetrated rate independent, elastic-perfectly plastic targets. The spherical and cylindrical, cavity-expansion approximations simplified the target analyses, so we obtained closed-form penetration equations. To verify our models, we performed terminal-ballistic experiments with 7.1-mm dia., 0.024 kg, marging steel rods and 152-mm dia., 6061-T651 aluminum targets. The models predicted penetration depths that were in reasonable agreement with the data for impact velocities between 0.4-1.4 km/s.

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible. Numerical results from both models showed the effect of compressibility.

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