DOI: 10.1051/jp2:1995210
J. Phys. II France 5 (1995) 1725-1738

On Low-Velocity Collisions of Viscoelastic Particles

Jan-Martin Hertzsch¹, Frank Spahn¹ and Nikolai V. Brilliantov<sup>2

1</sup>  Max-Planck-Arbeitsgruppe "Nichtlineare Dynamik", Universität Potsdam, Am Neuen Palais, PF 60 15 53, D-14415 Potsdam, Germany
²  Physics Department, Moscow State Univeristy, Moscow 119899, Russia

Abstract
The theory of the elastic contact of two bodies developed by Hertz [1] is generalized including the contribution of viscous effects to the total stress. A nonlinear differential equation for the compression is derived for particles with arbitrary curvature of their surfaces and is solved numerically for spherical particles. The resulting dependence of the normal restitution coefficient on the impact velocity is calculated and compared with experimental data for ice at low temperatures [2, 3]. A good agreement is found which allows to estimate unknown material constants in certain cases. An astrophysical application of the results is briefly discussed for the especially interesting case of icy particles in planetary rings.

Résumé
La théorie du contact élastique de deux corps developpée par Hertz [1] est généralisée tenant compte de la contribution des effects visqueux à la tension totale. Une équation différentielle nonlinéaire est derivée pour des particles dont les surfaces ont une courbure arbitraire. Elle est résolue numériquement dans le cas des particles sphériques. La dépendence du coefficient de restitution normale de la vitesse d'impact est calculée et comparée avec des données expérimentales obtenues pour la glace aux températures basses [2, 3]. Un bon accord est trouvé qui permet l'estimation des constantes du matériel dans certains cas. Une application astrophysique de nos résultats est discutée brèvement dans un cas d'intérêt particulier: des particles de glace dans des anneaux planétaires.

© Les Editions de Physique 1995

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