Electron. J. Differential Equations,
Vol. 2017 (2017), No. 299, pp. 117.
Analysis of a rateandstate friction problem with viscoelastic materials
Flavius Patrulescu, Mircea Sofonea
Abstract:
We 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
rateandstate 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
historydependent variational inequalities and nonlinear implicit
integral equations in Banach spaces.
Submitted September 21, 2017. Published December 5, 2017.
Math Subject Classifications: 74M15, 74M10, 74G25, 74G30, 49J40.
Key Words: Viscoelastic material; frictional contact; normal compliance;
rateandstate friction; differential variational inequality;
historydependent operator; weak solution.
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Flavius Patrulescu
Tiberiu Popoviciu Institute of Numerical Analysis
Romanian Academy, P.O. Box 681
400110 ClujNapoca, Romania
email: fpatrulescu@ictp.acad.ro


Mircea T. Sofonea
Laboratoire de Mathématiques et Physique
Université de Perpignan Via Domitia
52 Avenue de Paul Alduy
66 860 Perpignan, France
email: sofonea@univperp.fr

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