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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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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DOI: https://doi.org/10.21136/AM.2021.0308-19
Keywords
- viscoelastic material
- long memory
- adhesion
- quasistatic process
- Coulomb’s law of dry friction
- normal compliance
- the time-discretization method
- variational inequality