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On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.ORCID iD: 0000-0001-8460-0131
Department of Mechanical Engineering University of Michigan.
CEMEC-PoliBA.
2005 (English)In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 461, no 2057, 1261-1282 p.Article in journal (Refereed) Published
Abstract [en]

It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.

Place, publisher, year, edition, pages
2005. Vol. 461, no 2057, 1261-1282 p.
Keyword [en]
frictional heating; thermal contact; unilateral contact; linear thermoelasticity; existence, uniqueness
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-29078DOI: 10.1098/rspa.2004.1398Local ID: 14332OAI: oai:DiVA.org:liu-29078DiVA: diva2:249890
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2017-05-15

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Andersson, Lars-ErikKlarbring, Anders

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