Analytical Unloading Model for the Low Velocity Impact of Particles

The recovered process after elastoplastic impact plays an important role in estimating the energy dissipation induced by plasticity. The unloading process is assumed to be purely elastic and the pressure distribution at the initial unloading is approximately uniform. Based on these conditions, the recovered deformations of the spherical particle impact after fully unloading are solved by the elastic theory of a half-space loaded by the uniform pressure within a circular region. Then, the residual indentation is solved analytically from the recovered deformation. According to the analytical solution, an unloading impact model is proposed with the residual indentation based on the static elastic Hertzian relation. The assumptions of uniform pressure, solutions of the recovered deformation and residual indentation are verified by finite element results with a wide range of elastic-perfectly plastic materials. The unloading impact model can be used by the maximum force, indentation and radius and is validated by FE results. The present solutions and unloading law can comprehensively analyze and predict the unloading behavior of particle impact.