Geodesic
A frictional contact problem with adhesion for viscoelastic materials with long memory
Applications of Mathematics, Tome 66 (2021) no. 4, pp. 479-508

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We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization method, the Banach fixed point theorem and arguments of lower semicontinuity, compactness and monotonicity.
DOI : 10.21136/AM.2021.0308-19
Classification : 49J40, 74A55, 74D05, 74F25, 74H20
Keywords: viscoelastic material; long memory; adhesion; quasistatic process; Coulomb's law of dry friction; normal compliance; the time-discretization method; variational inequality 
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     title = {A frictional contact problem with adhesion for viscoelastic materials with long memory},
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Kasri, Abderrezak. A frictional contact problem with adhesion for viscoelastic materials with long memory. Applications of Mathematics, Tome 66 (2021) no. 4, pp. 479-508. doi: 10.21136/AM.2021.0308-19

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