Analysis of a rate-and-state friction problem with viscoelastic materials

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dc.contributor.authorPatrulescu, Flavius
dc.contributor.authorSofonea, Mircea
dc.date.accessioned2022-09-26T19:31:15Z
dc.date.available2022-09-26T19:31:15Z
dc.date.issued2017-12-05
dc.description.abstractWe consider a mathematical model which describes the frictional contact between a viscoelastic body and a foundation. The contact is modelled with normal compliance associated to a rate-and-state version of Coulomb's law of dry friction. We start by presenting a description of the friction law, together with some examples used in geophysics. Then we state the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. It is in a form of a differential variational inequality in which the unknowns are the displacement field and the surface state variable. Next, we prove the unique weak solvability of the problem. The proof is based on arguments of history-dependent variational inequalities and nonlinear implicit integral equations in Banach spaces.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationPǎtrulescu, F., & Sofonea, M. (2017). Analysis of a rate-and-state friction problem with viscoelastic materials. <i>Electronic Journal of Differential Equations, 2017</i>(299), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16171
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectViscoelastic material
dc.subjectFrictional contact
dc.subjectNormal compliance
dc.subjectRate-and-state friction
dc.subjectDifferential variational inequality
dc.subjectHistory-dependent operator
dc.subjectWeak solution
dc.titleAnalysis of a rate-and-state friction problem with viscoelastic materials
dc.typeArticle

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