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Quasistatic problems in contact mechanics

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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.
Opis fizyczny
  • Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
  • 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.
  • Amassad A., Shillor M. and Sofonea M. (1999b): A quasistatic contact problem with slipdependent coefficient of friction. - MMAS, Vol.22, pp.267-284.
  • Amassad A., Shillor M. and Sofonea M. (2001a): A nonlinear evolution inclusion in perfect plasticity with friction. - (preprint).
  • Amassad A., Rochdi M. and Shillor M. (2001b): A dynamic thermoviscoelastic contact with slip and temperature dependent friction. - (in preparation).
  • Andersson L.-E. (1991): A quasistatic frictional problem with normal compliance. - Nonlin. Anal., Vol.16, No.4, pp.347-370.
  • Andersson L.-E. and Klarbring A. (1997): On a class of limit states of frictional joints: formulation and existence theorem. - Quart. Appl. Math., Vol.LV, No.1, pp.9-87.
  • Andrews K.T., Kuttler K.L. and Shillor M. (1997): On the dynamic behaviour of a thermoviscoelastic body in frictional contact with a rigid obstacle. - Europ. J. Appl. Math., Vol.8, pp.417-436.
  • Andrews K.T., Klarbring A., Shillor M. and Wright S. (1997): A dynamic thermoviscoelastic contact problem with friction and wear. - Int. J. Eng. Sci., Vol.35, No.14, pp.1291- 1309.
  • Awbi B., M. Shillor and M. Sofonea (1999): A contact problem for Bingham fluid with friction. - Applic. Analysis, Vol.72, Vol.3-4, pp.469-484.
  • Awbi B., Shillor M. and Sofonea M. (2001): Dual formulation of a quasistatic viscoelastic contact problem with Tresca's friction law . - Applic. Anal. (to apper).
  • Chau O. (2000): Analyse Variationnelle et Numérique de Quelques Problèmes aux Limites en Mécanique du Contact. - Ph.D. Thesis, University of Perpignan.
  • Cocu M. (1984): Existence of solutions of Signorini problems with friction. - Int. J. Eng. Sci., Vol.22, No.7, pp.567-581.
  • Cocu M., Pratt E. and Raous M. (1996): Formulation and approximation of quasistatic frictional contact. - Int. J. Eng. Sci., Vol.34, No.7, pp.783-798.
  • Fernández-García J., Han W., Shillor M. and Sofonea M. (2000): Recent advances on variational and numerical analysis in contact mechanics. - Proc. MTNS 2000, Perpignan, France, June 19-23, published on CD-ROM.
  • Han W., Shillor M. and Sofonea M., Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage. - (to appear).
  • Jarusek J. and Eck C. (1996): Dynamic contact problems with friction in linear viscoelasticity. - C.R. Acad. Sci., Paris, Vol.322, pp.497-502.
  • Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. - Philadelphia: SIAM.
  • Klarbring A., Mikelic A. and Shillor M. (1988): Frictional contact problems with normal compliance. - Int. J. Eng. Sci., Vol.26, No.8, pp.811-832.
  • 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.
  • 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.
  • Martins J.A.C. and Oden J.T. (1987): Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. - Nonlin. Anal., Vol.11, No.3, pp.407-428.
  • Raous M., Jean M. and Moreau J.J. (Eds.) (1995): Contact Mechanics. - New York: Plenum Press.
  • Rabinowicz E. (1995): Friction and Wear of Materials, 2nd Ed. - New York: Wiley.
  • Rochdi M. and Shillor M. (2001): Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity. - Q. Appl. Math. (to appear).
  • 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.
  • Rochdi M., Shillor M. and Sofonea M. (1998b): Quasistatic viscoelastic contact with normal compliance and friction. - J. Elasticity, Vol.51, pp.105-126.
  • Shillor M. (Ed.) (1998): Recent Advances in Contact Mechanics. - Special issue of Math. Comput. Modelling, Vol.28, No.4-8.
  • Shillor M. and Sofonea M. (2001): A quasistatic viscoelastic contact problem with friction. - Inl. J. Eng. Sci. (to appear).
  • Sofonea M. and Shillor M. (2001): Variational analysis of quasistatic viscoplastic contact problems with friction. - Comm. Appl. Analysis (to appear).
  • Shillor M., Sofonea M. and Telega J.J. (2001): Review of recent results on quasistatic contact (in preparation).
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