Motion model of spherical fragments penetrating gelatin and sensitivity analysis of fragment parameters

To reveal the injury mechanism of spherical fragments to human tissue, gelatin was used as a substitute for human tissue. Based on the theory of dynamic cavity expansion, the segmental motion theoretical model of spherical fragments penetrating gelatin was established by considering the velocity attenuation of spherical fragments in the stage of incomplete entering stage, and the motion law of spherical fragments penetrating gelatin was studied. The correctness of the model was verified by the experiments of steel balls and tungsten balls penetrating gelatin, and the optimal drag coefficients in the model were solved. The sources of errors in the theoretical calculation process were analyzed, and the expression of dimensionless penetration depth was derived. A sensitivity analysis of the influence of spherical fragment parameters (diameter, density and velocity) on the penetration depth was carried out by using the Sobol' method. The results show that the motion model can well simulate the motion law of spherical fragments. The velocity attenuation of low-density spherical fragments in the incomplete entering stage cannot be ignored. The sensitivity of spherical fragment parameters to the effect of penetration depth is in descending order of velocity, density and diameter.