Geodesic
Study of a viscoelastic frictional contact problem with adhesion
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 2, pp. 257-272.

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We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the weak solution under a certain condition on the coefficient of friction. The proof is based on time-dependent variational inequalities, differential equations and Banach fixed point theorem.
Classification : 47J20, 49J40, 74M10, 74M15
Keywords: viscoelastic; normal compliance; adhesion; frictional; variational inequality; weak solution 
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Touzaline, Arezki. Study of a viscoelastic frictional contact problem with adhesion. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 2, pp. 257-272. http://geodesic.mathdoc.fr/item/CMUC_2011__52_2_a5/