A spherical cavity expansion model of large elastic deformation and its application to ballistic gelatin penetration problems

Analytic solutions of stress field for quasi-static expansion of spherical cavity in incompressible soft medium are derived, in which large elastic deformation is modeled by the Mooney-Rivlin constitutive equation and the failure behavior by elastic-fracture. As a consequence, the work needed to open unit volume of cavity in infinite medium, Ps, is obtained, which reflects the material's strength and is widely used in studying penetration problems. Energy partition between the elastic and fracture regions is analyzed. Uniaxial compression and simple shear experiments were carried out to determine the moduli in Mooney-Rivlin model at low strain rates for 10 wt% ballistic gelatin at 4 °C, and the failure mode is determined to be elastic-fracture as the stretch ratio exceeds a critical value in the range of 1.5-2.0. For high loading rates, available results from the split Hopkinson pressure bar (SHPB) experiments are carefully examined and assessed, and linear increasing of Ps with the strain rate is suggested. The application of Ps model to ballistic penetration problems is presented and discussed, and with a properly defined characteristic strain rate, the model of Ps reasonably agree with the experiments in terms of the maximum cavity volumes in 10 wt% ballistic gelatin penetrated by fragments of various shapes and a bullet.