A dissipative force between colliding viscoelastic bodies: Rigorous approach

TL;DR

This paper presents a rigorous analytical approach to derive the dissipative force during collisions of viscoelastic bodies, improving upon the quasi-static approximation by accounting for strain and strain rate simultaneously.

Contribution

It introduces a perturbation scheme for continuum mechanics that accurately models dissipation in viscoelastic collisions, addressing limitations of previous approximations.

Findings

Derived a new dissipative force expression based on deformation and material parameters.

Showed the new force differs significantly from the quasi-static approximation.

Provided a framework applicable to other bulk dissipation problems in continuum mechanics.

Abstract

A collision of viscoelastic bodies is analysed within a mathematically rigorous approach. We develop a perturbation scheme to solve continuum mechanics equation, which deals simultaneously with strain and strain rate in the bulk of the bodies' material. We derive dissipative force that acts between particles and express it in terms of particles' deformation, deformation rate and material parameters. It differs noticeably from the currently used dissipative force, found within the quasi-static approximation and does not suffer from inconsistencies of this approximation. The proposed approach may be used for other continuum mechanics problems where the bulk dissipation is addressed.