A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 1, page 85-97
  • ISSN: 0010-2628

Abstract

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We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.

How to cite

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Touzaline, Arezki. "A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 85-97. <http://eudml.org/doc/37746>.

@article{Touzaline2010,
abstract = {We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.},
author = {Touzaline, Arezki},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {viscoelastic materials; adhesion; Tresca's friction; fixed point; weak solution; contact problem; viscoelastic material; Tresca's friction; adhesion; existence; unicity; Banach fixed point theorem},
language = {eng},
number = {1},
pages = {85-97},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials},
url = {http://eudml.org/doc/37746},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Touzaline, Arezki
TI - A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 85
EP - 97
AB - We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result of the weak solution. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.
LA - eng
KW - viscoelastic materials; adhesion; Tresca's friction; fixed point; weak solution; contact problem; viscoelastic material; Tresca's friction; adhesion; existence; unicity; Banach fixed point theorem
UR - http://eudml.org/doc/37746
ER -

References

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