A study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline. "A study of a unilateral and adhesive contact problem with normal compliance." Applicationes Mathematicae 41.4 (2014): 385-402. <http://eudml.org/doc/279933>.

@article{ArezkiTouzaline2014,
abstract = {The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the friction coefficient is small enough. The technique of proof is based on time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. We also study a penalized and regularized problem which admits at least one solution and prove its convergence to the solution of the model when the penalization and regularization parameter tends to zero.},
author = {Arezki Touzaline},
journal = {Applicationes Mathematicae},
keywords = {elastic; normal compliance; adhesion; friction; unilateral},
language = {eng},
number = {4},
pages = {385-402},
title = {A study of a unilateral and adhesive contact problem with normal compliance},
url = {http://eudml.org/doc/279933},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Arezki Touzaline
TI - A study of a unilateral and adhesive contact problem with normal compliance
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 4
SP - 385
EP - 402
AB - The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the friction coefficient is small enough. The technique of proof is based on time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. We also study a penalized and regularized problem which admits at least one solution and prove its convergence to the solution of the model when the penalization and regularization parameter tends to zero.
LA - eng
KW - elastic; normal compliance; adhesion; friction; unilateral
UR - http://eudml.org/doc/279933
ER -