Collision of viscoelastic bodies: Rigorous derivation of dissipative force

TL;DR

This paper develops a rigorous theoretical framework to accurately derive dissipative forces during collisions of viscoelastic bodies, accounting for deformation and deformation rate without the limitations of previous quasi-static models.

Contribution

It introduces a mathematically rigorous perturbation scheme to derive dissipative forces, improving upon previous approximations by accounting for bulk dissipation effects.

Findings

Derived a dissipative force expression dependent on deformation and rate.

Overcame limitations of quasi-static approximation.

Provided a consistent continuum mechanics solution.

Abstract

We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large, to avoid plastic deformations and fragmentation at the impact. The bodies may be of an arbitrary convex shape and of different materials. We develop a mathematically rigorous perturbation scheme to solve the continuum mechanics equation that deals with both displacement and displacement rate fields and accounts for the dissipation in the bulk of the material. The perturbative solution of this equation allows to go beyond the previously used quasi-static approximation and obtain the dissipative force. This force does not suffer from the physical inconsistencies of the latter approximation and depends on particle deformation and deformation rate.