A resistance force model for spherical projectiles penetrating ballistic gelatin based on cavity expansion theory

Abstract

To investigate the penetration mechanism of spherical projectiles into soft tissues, ballistic gelatin was used as tissue substitute in ballistic tests. A theoretical motion model was established based on the cavity expansion theory. We first presented a quasi-static cylindrical cavity expansion model for the radial stress at the cavity wall of a cracked-hyperelastic material. The pressure on the cavity surface, PS, was also defined as the energy required to open a unit volume in the medium quasi-statically. Based on this interpretation, we proposed an approximate expression for the dynamic pressure, P, acting on the surface of the cavity by analyzing the energy transformation and conservation. Then, based on the analysis and solutions of the cylindrical cavity expansion model, we obtained a resistance force model for spherical projectiles, which consisted of an inertial term and a rate-dependent strength term. Subsequently, ballistic tests, in which gelatin blocks were penetrated by spherical projectiles of different materials and sizes, were analyzed, and the parameters in the resistance model were identified using the test results obtained from the 3 mm steel projectile. Further, the ability of the motion model to describe the motion of spherical projectiles penetrating ballistic gelatin was verified by comparing the calculated and measured results from projectiles of different materials and sizes. The proposed motion model based on the cavity expansion theory can therefore provide a basis for understanding the interaction of small arms ammunition and soft tissues.