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A frictional contact problem with adhesion for viscoelastic materials with long memory

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Abstract

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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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université 20 Août 1955 - Skikda, B.P. 26 Route El-Hadaiek, Skikda, 21000, Algeria

    Abderrezak Kasri

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  1. Abderrezak Kasri
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Correspondence to Abderrezak Kasri.

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Kasri, A. A frictional contact problem with adhesion for viscoelastic materials with long memory. Appl Math 66, 479–508 (2021). https://doi.org/10.21136/AM.2021.0308-19

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