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

Abderrezak Kasri

Applications of Mathematics (2021)

  • Volume: 66, Issue: 4, page 479-508
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Kasri, Abderrezak. "A frictional contact problem with adhesion for viscoelastic materials with long memory." Applications of Mathematics 66.4 (2021): 479-508. <http://eudml.org/doc/297532>.

@article{Kasri2021,
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.},
author = {Kasri, Abderrezak},
journal = {Applications of Mathematics},
keywords = {viscoelastic material; long memory; adhesion; quasistatic process; Coulomb's law of dry friction; normal compliance; the time-discretization method; variational inequality},
language = {eng},
number = {4},
pages = {479-508},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A frictional contact problem with adhesion for viscoelastic materials with long memory},
url = {http://eudml.org/doc/297532},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Kasri, Abderrezak
TI - A frictional contact problem with adhesion for viscoelastic materials with long memory
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 479
EP - 508
AB - 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.
LA - eng
KW - viscoelastic material; long memory; adhesion; quasistatic process; Coulomb's law of dry friction; normal compliance; the time-discretization method; variational inequality
UR - http://eudml.org/doc/297532
ER -

References

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