Cavity dynamics and drag force of high-speed penetration of rigid spheres into 10wt% gelatin

Cavity expansion-contraction in the high-speed penetration of rigid spheres into 10wt% gelatin targets at 4 °C is modeled by assuming the energy conservation for each cross sectional layer along the penetration trajectory. A simple analytic solution is obtained. By adopting an approximate characteristic velocity or mean expansion-contraction speed (≈10 m/s), this solution yields self-similar cavity wall movements for various sizes of penetrating spheres along the penetration trajectory. The modelʹs description is well confirmed by experimental high-speed video observations. The model is further transformed into the drag force in terms of penetration velocity based on experimentally observed maximum cavity radii and the separation angles of gelatin from spheres. The key parameter is the work needed to open unit volume of cavity in gelatin, which is found to be linearly increasing with the characteristic strain-rate, defined by the characteristic velocity over the cavityʹs local maximum radius. The modelʹs predictability for drag forces is well confirmed by penetration experiments using steel-spheres of four sizes and one tungsten-sphere.