Critical Plate Thickness for Energy Dissipation During Sphere–Plate Elastoplastic Impact Involving Flexural Vibrations

Solid processing storage and conveying units (e.g., hoppers, silos, tumblers, etc.) often involve the collision of granular media with relatively thin walls. Therefore, the impact of a sphere with a thin plate is a problem with both fundamental and practical importance. In the present work, the normal elastoplastic impact between a sphere and a thin plate is analyzed using an explicit finite element method (FEM). The impact involves plastic deformation and flexural vibrations, which when combined results in significant energy dissipation. One way to quantify the energy dissipation is to employ the coefficient of restitution (COR), which is also a key input parameter needed in various granular flow models. The results were validated against the available experimental data. It is observed that, in addition to material properties and impact parameters, the energy dissipation is strongly dependent on the ratio of plate thickness to sphere diameter. A comprehensive parametric study is conducted to evaluate the effect of material properties, geometry, and impact parameters on the energy dissipation. For the impact velocities commonly observed in granular systems (V = 5 m/s or less), it was determined that the energy lost to flexural vibrations can be neglected if the plate thickness is more than twice the sphere diameter, i.e., t_cr > 2d. In this scenario, the mode of energy dissipated is primarily due to the plasticity effects.