Volume 109, Number 1, January 2015
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||22 January 2015|
A dissipative force between colliding viscoelastic bodies: Rigorous approach
1 Department of Mathematics, University of Leicester - Leicester LE1 7RH, UK
2 Institute of Continuous Media Mechanics, UB RAS - Perm 614013, Russia
3 Theoretical Physics Department, Perm State University - Perm 614990, Russia
Received: 10 July 2014
Accepted: 19 December 2014
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.
PACS: 45.70.-n – Granular systems / 45.50.Tn – Collisions
© EPLA, 2015
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