# Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

• Volume: 26, Issue: 4, page 415-435
• ISSN: 1233-7234

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## Abstract

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We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.

## How to cite

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Han, Weimin, and Sofonea, Mircea. "Analysis and numerical approximation of an elastic frictional contact problem with normal compliance." Applicationes Mathematicae 26.4 (1999): 415-435. <http://eudml.org/doc/219249>.

@article{Han1999,
abstract = {We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.},
author = {Han, Weimin, Sofonea, Mircea},
journal = {Applicationes Mathematicae},
keywords = {normal compliance; finite element approximation; Coulomb's law; error estimates; frictional contact; variational inequality; fixed point},
language = {eng},
number = {4},
pages = {415-435},
title = {Analysis and numerical approximation of an elastic frictional contact problem with normal compliance},
url = {http://eudml.org/doc/219249},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Han, Weimin
AU - Sofonea, Mircea
TI - Analysis and numerical approximation of an elastic frictional contact problem with normal compliance
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 4
SP - 415
EP - 435
AB - We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.
LA - eng
KW - normal compliance; finite element approximation; Coulomb's law; error estimates; frictional contact; variational inequality; fixed point
UR - http://eudml.org/doc/219249
ER -

## References

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12. [12] J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elastoplastic Bodies$:$ An Introduction, Elsevier, Amsterdam, 1981.
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14. [14] M. Rochdi, M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with normal compliance and friction, J. Elasticity 51 (1998), 105-126. Zbl0921.73231
15. [15] M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with friction, Int. J. Engrg. Sci., to appear. Zbl1210.74132
16. [16] S N. Strömberg, Continuum Thermodynamics of Contact$,$ Friction and Wear, Ph.D. Thesis, Linköping University, 1995.
17. [17] N. Strömberg, L. Johansson and A. Klarbring, Derivation and analysis of a generalized standard model for contact friction and wear, Int. J. Solids Structures 33 (1996), 1817-1836. Zbl0926.74012
18. [18] Z E. Zeidler, Nonlinear Functional Analysis and its Applications. IV$:$ Applications to Mathematical Physics, Springer, New York, 1988. Zbl0648.47036

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