A dissipative force between colliding viscoelastic bodies: Rigorous results

Nikolay V. Brilliantov, Anastasiya V. Pimenova, Denis S. Goldobin

Published 2014-10-13Version 1

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