Hertz Beyond Belief

TL;DR

This paper investigates the accuracy of Hertz's elastic collision theory using a viscoelastic model, revealing its robustness despite energy dissipation and explaining size-dependent yield strength effects.

Contribution

It introduces a viscoelastic model that explains Hertz's theory validity under energy loss and clarifies size-dependent yield strength in collisions.

Findings

Hertz's theory remains accurate despite 40% energy loss.

Collision time and contact area weakly depend on impact velocity.

Larger objects dissipate less energy, affecting yield strength.

Abstract

We examine the validity of Hertz's linear elastic theory for central collisions using a viscoelastic model. This model explains why Hertz's theory is accurate in predicting the collision time and maximum contact area even when $40\%$ of the kinetic energy is lost due to viscous dissipation. The main reason is that both the collision time and maximum contact area have a very weak dependence on the impact velocity. Moreover, we show that colliding objects exhibit an apparent size dependent yield strength, which results from larger objects dissipating less energy at a given impact velocity.