Unloading of Low Velocity Impact Between Elastic and Elastic-Plastic Bodies

The unloading process of an elastic sphere impacting an elastic-perfectly plastic half-space under low velocity and frictionless conditions is deeply studied in the light of finite element (Eh) analysis. The unloading in the Eh simulations ranges from elastic-plastic to fully plastic deformation regimes by designed impact velocities and material properties. The cavity profiles after unloading are measured from the FE simulations based on the spherical residual cavity validation. An analytical expression of the radius of spherical residual cavity is derived from the fitting method. The residual radius of curvature is determined by combining its physical definition with the analytical expression. A new revised Hertz unloading model is suggested, which is validated numerically and experimentally.