Impact of a rigid sphere onto an elastic membrane

Abstract

We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our model predictions are validated against our direct experimental measurements. Moreover, we identify new phenomena regarding the behaviour of the coefficient of restitution for low impact velocities, the possibility of multiple contacts during a single rebound, and energy recovery on subsequent bounces. Insight obtained from this model problem in contact mechanics can inform ongoing efforts towards the development of predictive models for contact problems that arise naturally in multiple engineering applications.

Similarity solutions in elastohydrodynamic bouncing

“…drop impacts (Mandre, Mani & Brenner 2009) or elastic capsules (Jambon-Puillet, Jones & Brun 2020; Rémond et al 2022), or changing the impacted surface, e.g. stretched membranes (Courbin et al 2006; Verzicco & Querzoli 2021; Agüero et al 2022) or liquid pool (Galeano-Rios et al 2021; Alventosa, Cimpeanu & Harris 2023; Sykes et al 2023).…”