Review of Quasi-Analytical and Cavity Expansion Methods for Projectile Penetration of Concrete Targets

Abstract

This paper presents state-of-the art review on the development of quasi-analytical and cavity expansion methods that are used to determine projectile penetration of targets, dating back to the middle of the 20^th century. The paper briefly describes the three general approaches used in determining the impact mechanics of targets subjected to projectiles; quasi-analytical, analytical and numerical approaches. Then, the paper provides detailed review of quasi-analytical and analytical methods because they are quite important in characterizing small-scale or large-scale experimental data; developing a basic understanding of the penetration mechanics; and making faster predictions of global parameters such as penetration depth within the limits of applicability of the methods. Quasi-analytical methods are employed when the physical phenomenon being described is highly complex and dependent upon variables that are difficult to isolate and control. These methods often have, at their core, fundamental basis in physics such as Newton's second law of motion. A list of well-known quasi-analytical equations used for determining depth of penetration into concrete targets is provided. The Sandia National Laboratory equations are provided as an example because they are developed from comprehensive database of tests. Analytical methods attempt to provide a correlation between many of the variables in the phenomenon being modeled. They are typically based on solving differential equations of continuum mechanics. However, these methods typically rely on assuming material properties which are necessary to arrive at closed-form solutions. A detailed review of analytical equations that are based on the cavity expansion method, supplemented with experimental data obtained from penetration experiments, is provided. Although the majority of the review includes analytical equations used for concrete targets, these equations trace their origin in the earlier works of penetration of metal and soil targets, which are included in cavity expansion method chronology provided in the paper.