Quasistatic problems in contact mechanics

Meir Shillor

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 1, page 189-204
  • ISSN: 1641-876X

Abstract

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We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.

How to cite

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Shillor, Meir. "Quasistatic problems in contact mechanics." International Journal of Applied Mathematics and Computer Science 11.1 (2001): 189-204. <http://eudml.org/doc/207499>.

@article{Shillor2001,
abstract = {We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.},
author = {Shillor, Meir},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {normal compliance; quasistatic contact; friction; unilateral contact; wear; thermoriscoelastic; quasistatic contact problems; deformable body; foundation; frictional contact; thermal effects; wear of contacting surfaces; variational formulation},
language = {eng},
number = {1},
pages = {189-204},
title = {Quasistatic problems in contact mechanics},
url = {http://eudml.org/doc/207499},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Shillor, Meir
TI - Quasistatic problems in contact mechanics
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 1
SP - 189
EP - 204
AB - We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.
LA - eng
KW - normal compliance; quasistatic contact; friction; unilateral contact; wear; thermoriscoelastic; quasistatic contact problems; deformable body; foundation; frictional contact; thermal effects; wear of contacting surfaces; variational formulation
UR - http://eudml.org/doc/207499
ER -

References

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  1. Amassad A., Shillor M. and Sofonea M. (1999a): A quasistatic contact problem for an elastic perfectly plastic body with Tresca's friction. - Nonlin. Anal., Vol.35, pp.95-109. Zbl0923.73054
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  4. Amassad A., Rochdi M. and Shillor M. (2001b): A dynamic thermoviscoelastic contact with slip and temperature dependent friction. - (in preparation). 
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  15. Han W., Shillor M. and Sofonea M., Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage. - (to appear). Zbl0999.74087
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  19. Klarbring A., Mikelic A. and Shillor M. (1991): A global existence result for the quasistatic frictional contact problem with normal compliance, In: Unilateral Problems in Structural Analysis, Vol.4 (G. Del Piero and F. Maceri, Eds.). - Boston: Birkhäuser, pp.85- a 111. Zbl0761.73104
  20. Kuttler K.L. and Shillor M. (1999): Set-valued pseudomonotone maps and degenerate evolution inclusions. - Comm. Contemp. Math., Vol.1, No.1, pp.87-123. Zbl0959.34049
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  24. Rochdi M. and Shillor M. (2001): Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity. - Q. Appl. Math. (to appear). Zbl1151.74397
  25. Rochdi M., Shillor M. and Sofonea M., (1998a): A quasistatic contact problem with directional friction and damped response. - Applic. Anal., Vol.68, No.3-4, pp.409-422. Zbl0904.73055
  26. Rochdi M., Shillor M. and Sofonea M. (1998b): Quasistatic viscoelastic contact with normal compliance and friction. - J. Elasticity, Vol.51, pp.105-126. Zbl0921.73231
  27. Shillor M. (Ed.) (1998): Recent Advances in Contact Mechanics. - Special issue of Math. Comput. Modelling, Vol.28, No.4-8. 
  28. Shillor M. and Sofonea M. (2001): A quasistatic viscoelastic contact problem with friction. - Inl. J. Eng. Sci. (to appear). Zbl1210.74132
  29. Sofonea M. and Shillor M. (2001): Variational analysis of quasistatic viscoplastic contact problems with friction. - Comm. Appl. Analysis (to appear). Zbl1084.74541
  30. Shillor M., Sofonea M. and Telega J.J. (2001): Review of recent results on quasistatic contact (in preparation). 

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