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
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.
Submitted September 21, 2017. Published December 5, 2017.
Math Subject Classifications: 74M15, 74M10, 74G25, 74G30, 49J40.
Key Words: Viscoelastic material; frictional contact; normal compliance;
rate-and-state friction; differential variational inequality;
history-dependent operator; weak solution.
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Flavius Patrulescu Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy, P.O. Box 68-1 400110 Cluj-Napoca, Romania email: fpatrulescu@ictp.acad.ro |
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Mircea T. Sofonea Laboratoire de Mathématiques et Physique Université de Perpignan Via Domitia 52 Avenue de Paul Alduy 66 860 Perpignan, France email: sofonea@univ-perp.fr |
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