Semi-Analytical Model for Elastoplastic Impact of Sphere on Plate

Abstract

During the impact of a sphere on a large plate, the initial kinetic energy can be dissipated through two mechanisms: the plastic work done at the contact point and the flexural wave dissipated throughout the plate. To date, no model has adequately accounted for energy loss from both factors. In this paper, we propose a new model for the elastoplastic impact of a sphere on a large plate by combining the vibration of large plates with the elastoplastic contact model. By solving the governing equation, we demonstrate that such impacts are controlled by two non-dimensional parameters: one related to the plate's flexibility and the other to the material's yielding stress. Furthermore, we derive semi-analytical solutions for the maximum impact depth, maximum contact force, and the coefficient of restitution. Additionally, we discuss the competitive mechanisms of energy dissipation through local plastic deformation and flexural wave propagation.

Keywords: Sphere-plate impact, Flexural wave, Contact plasticity, Maximum indentation depth, Coefficient of restitution