Penetration dynamics of steel spheres into a ballistic gelatin: Experiments, nondimensional analysis, and finite element modeling

Abstract

Ballistic gelatin is widely used as a simulant of soft tissues, and its dynamic responses to high-speed projectile penetration are critical for understanding soft tissue damage, wound ballistics, and protection gear design. Here, we investigate penetration dynamics of spherical steel projectiles with different diameters into a ballistic gelatin at different incident velocities. The projectile diameter ranges from 1 mm to 5 mm, and the incident velocity, from 50 m s−1 to 400 m s−1. Penetration dynamics is captured with high-speed photography. A power-law relation is found between the maximum penetration depth and projectile kinetic energy at high incident velocities, but not at intermediate and low velocities. Nondimensional analysis is applied to the penetration depth; a general relation is established for nondimensional maximum penetration depth as a function of projectile density, projectile diameter and projectile incident velocity for low-, intermediate- and high-speed penetration, and this relation can accurately describe the experiments. The drag force of projectile is analyzed to explain the relation between projectile acceleration and velocity. In addition, a calibrated finite element model reproduces well experimental observations such as the maximum penetration depth and projectile trajectory.