Background: Methods for describing physics of impact and ballistics have been developed over a number of decades. These include analytical mathematical representations as well as modern computer simulations.
Objective: Recent and historic developments towards modeling of impact phenomena pertinent to terminal ballistic events are summarized and compared. Two classes of physical problem are of focus: impact and penetration of metallic and/or ceramic targets by projectiles, and propagation of planar shock waves through solid material specimens induced by collision with flyer plates or by explosive loading.
Method: The projectile-target problem is analyzed from perspectives of classical hydrodynamics, extensions accounting for strength, and fully resolved explicit dynamics simulations. The planar impact test is studied from perspectives of analytical solutions to Rankine-Hugoniot equations, steady wave analysis, and dynamic finite element simulations of shock waves in material microstructures. Key features of each approach are critically compared.
Results: The two classes of physical problem are inherently related since material properties obtained from analysis of the latter experiments are typical input for models of the former problem involving ballistic penetration. Patents to computer methods and ballistic protection systems are noted.
Conclusion: Reduced order models are shown to provide efficient, but often approximate, solutions giving insight into general trends. Modern, fully resolved calculations appear to be the only viable route to design and optimization of novel materials or structures with heterogeneous properties or complex geometries.