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

Applicationes Mathematicae (2010)

- Volume: 37, Issue: 1, page 39-52
- ISSN: 1233-7234

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topArezki Touzaline. "A quasistatic contact problem with adhesion and friction for viscoelastic materials." Applicationes Mathematicae 37.1 (2010): 39-52. <http://eudml.org/doc/279991>.

@article{ArezkiTouzaline2010,

abstract = {We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness of a weak solution if the friction coefficient is sufficiently small. The proof is based on time-dependent variational inequalities, differential equations and the Banach fixed point theorem.},

author = {Arezki Touzaline},

journal = {Applicationes Mathematicae},

keywords = {variational inequalities; weak solution; existence; uniqueness; Banach fixed point theorem},

language = {eng},

number = {1},

pages = {39-52},

title = {A quasistatic contact problem with adhesion and friction for viscoelastic materials},

url = {http://eudml.org/doc/279991},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Arezki Touzaline

TI - A quasistatic contact problem with adhesion and friction for viscoelastic materials

JO - Applicationes Mathematicae

PY - 2010

VL - 37

IS - 1

SP - 39

EP - 52

AB - We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness of a weak solution if the friction coefficient is sufficiently small. The proof is based on time-dependent variational inequalities, differential equations and the Banach fixed point theorem.

LA - eng

KW - variational inequalities; weak solution; existence; uniqueness; Banach fixed point theorem

UR - http://eudml.org/doc/279991

ER -

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