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Rock’s Interface Problem Including Adhesion

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Nonsmooth/Nonconvex Mechanics

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 50))

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Abstract

A rock’s dynamic contact model taking into account friction and adhesion phenomena is discussed. It consists of a hemivariational inequality because of the adhesion process. A weak solution is obtained as a limit of a sequence of solutions to some regularized problems after establishing the necessary estimates.

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References

  • Frémond, M. (1982). Adhésion et contact unilatéral, in Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, Waterloo, Canada.

    Google Scholar 

  • Frémond, M. (1987). Adhérance des solides, Journal de Mécanique Théorique et Appliquée, 6(3):383–407.

    MATH  Google Scholar 

  • Frémond, M. Sacco, E., Point, N. and Tien, J.M. (1996). Contact with adhesion, AMSEPD-Vol. 76, ESDA Proceedings of the 1996 Eng. Syst. Design and Analysis Conference, pp. 151–156.

    Google Scholar 

  • Goeleven, D., and Motreanu, D. (1999). A mathematical approach to the rock interface problem, Journal of Elasticity, 55(2):79–98.

    Article  MathSciNet  MATH  Google Scholar 

  • Klarbring, A., Mikelic, A., and Shillor, M. (1988). Frictional contact problems with normal compliance, International Journal of Engineering Sciences, 26(8):811–832.

    Article  MathSciNet  MATH  Google Scholar 

  • Kikuchi, N., and Oden, T.J. (1988). Contact problems in elasticity, SIAM, Philadelphia.

    MATH  Google Scholar 

  • Kuttler, K.L., and Shillor, M. (1999). Set-valued pseudomonotone maps and degenerate evolution inclusions, Communications in Contemporary Mathematics 1(1):87–123.

    Article  MathSciNet  MATH  Google Scholar 

  • Kuttler, K.L., and Shillor, M. (1998). Dynamic contact with normal compliance wear and discontinuous friction coefficient, preprint.

    Google Scholar 

  • Lions, J.L. (1969). Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris.

    MATH  Google Scholar 

  • Martins, J.A.C., and Oden, J.T. (1987). Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws, Nonlinear Analysis. Theory, Methods and Applications, 11(3):407–428.

    Article  MathSciNet  Google Scholar 

  • Moreau, J.J. (1968). La notion de sur-potentiel et les liaisons unilatérales en élastostatiques, C. R. Acad. Sci., Paris, Serie A, 267:954–957.

    MathSciNet  MATH  Google Scholar 

  • Panagiotopoulos, P.D. (1985). Inequality problems in mechanics and applications, Birkhaüser, Basel.

    MATH  Google Scholar 

  • Point, N. (1988). Unilateral contact with adhesion, Mathematical Methods in Applied Sciences, 10:367–381.

    Article  MathSciNet  MATH  Google Scholar 

  • Raous, M., Cangémi, L., and Cocu, M. (2000). A consistent model coupling adhesion, friction, and unilaterlal contact, Computer Methods in Applied Mechanics Engineering, 177 (3–4):383–400.

    Article  Google Scholar 

  • Rochdi, M., Shillor, M., and Sofonea, M. (1998). Quasistatic viscoelastic contact with normal compliance and friction, Journal of Elasticity, 51:105–126.

    Article  MathSciNet  MATH  Google Scholar 

  • Seidman T.I., (1989). The transient semiconductor problem with generation terms, II, in nonlinear semigroups, partial differential equations and attractors, Springer Lecture Notes in Mathematics, 1394:185–198.

    Article  MathSciNet  Google Scholar 

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Dedicated to the memory of Professor P.D. Panagiotopoulos.

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© 2001 Kluwer Academic Publishers

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Dumont, Y., Goeleven, D., Kuttler, K.L., Rochdi, M., Shillor, M. (2001). Rock’s Interface Problem Including Adhesion. In: Gao, D.Y., Ogden, R.W., Stavroulakis, G.E. (eds) Nonsmooth/Nonconvex Mechanics. Nonconvex Optimization and Its Applications, vol 50. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0275-9_4

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  • DOI: https://doi.org/10.1007/978-1-4613-0275-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7973-7

  • Online ISBN: 978-1-4613-0275-9

  • eBook Packages: Springer Book Archive

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