Collision of circular/elliptic rings and spheroid shells with a rigid surface

Abstract

Тhe moving free-body impact occurs in various engineering applications ranging from sports ball's rebound from ground and collision of granular materials to cars’ crashing on solid barriers. In those situations, impact duration, energy transformation and energy absorption, rebound behaviour and thereafter coefficient of restitution are the most important characteristics in concern. The dynamic responses of rings with circular and elliptic shapes and shells with spherical and ellipsoidal shapes colliding with a rigid target are studied to clarify the influence of their shapes on the coefficient of restitution ($CoR$). The structures are made of elastic-plastic materials with the properties referring to Aluminium alloy 6061-T6 and Nylon. The rings with different shapes and spheroid shells with different shapes have equal masses, respectively. An energy partitioning analysis is employed as a tool to explain the variation of the $CoR$ when colliding velocities up to 40 m/s are applied to the rings and colliding velocities up to 25 m/s are applied to the shells. Because of the flexibility of the analyzed structures, attention is paid to the effects of the structural vibrations and elasticity. Distinct differences between the dynamic responses of the rings and spheroid shells are observed caused by their different flexibility.

It is established that the coefficient of restitution of the analyzed structures is mainly governed by the translational motion. The shapes and material properties of both the rings and shells significantly influence their coefficient of restitution. The $CoR$ of the rings in the elastic range is greatly reduced by their vibrational motion when the largest $CoR$ is observed in the circular ring while the smallest one is detected for the ring in a vertical ellipse shape. The spheroid shells have coefficients of restitution close to one in the elastic range due to the negligible elastic vibrations. In the elastic-plastic range, the $CoR$ of the rings is strongly influenced by the deformation history due to their large global deformation. The $CoRs$ of the shells with different shapes are influenced mainly by the local deformations in the contact area where the largest $CoR$ is observed in the oblate spheroid shell while the smallest one is observed in the prolate spheroid shell within the entire range of the analyzed impact velocities. The parametric analysis is conducted by using FE simulations facilitated by Abaqus/Explicit.