Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Energy balance for viscoelastic bodies in frictionless contact

Author: David E. Stewart
Journal: Quart. Appl. Math. 67 (2009), 735-743
MSC (2000): Primary 74M20; Secondary 35L85, 49J40
DOI: https://doi.org/10.1090/S0033-569X-09-01161-8
Published electronically: May 14, 2009
MathSciNet review: 2588233
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Abstract: In this paper it is shown that the change in the energy for a linearly viscoelastic body (with Kelvin–Voigt type viscosity) in frictionless contact with a rigid obstacle can be accounted for by viscous losses and the work done by external forces. Thus there is no change in the energy due to impacts, unlike the case of rigid-body dynamics. The result can be extended to a wide class of dynamic viscoelastic boundary thin obstacle problems of similar type.

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Additional Information

David E. Stewart
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: dstewart@math.uiowa.edu

Keywords: Impact, viscoelasticity, energy balance, dynamic variational inequalities
Received by editor(s): July 25, 2008
Published electronically: May 14, 2009
Additional Notes: This work was supported in part by the NSF under grant DMS-0139709.
Article copyright: © Copyright 2009 Brown University