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Keywords:
viscoelastic material; long memory; adhesion; quasistatic process; Coulomb's law of dry friction; normal compliance; the time-discretization method; variational inequality
viscoelastic material; long memory; adhesion; quasistatic process; Coulomb's law of dry friction; normal compliance; the time-discretization method; variational inequality
Summary:
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.
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