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References
J.J. Kalker, Variational principles of contact elastostatics, J. Inst. Math. Appl., Vol. 20 (1977), 199–219.
N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, (1988).
For more details of thisargument see J.R. Barber, Determining the contact area in elastic contact problems, J. Strain Analysis, Vol. 9 (1974), 230–232.
R.T. Shield, Load-displacement relations for elastic bodies, Z.angew.Math.Phyz., Vol. 18 (1967), pp. 682–693.
D.A. Spence, An eigenvalue problem for elastic contact with finite friction, Proc. Cambridge Phil. Soc., Vol. 73 (1973), 249–268, has shown that this argument also extends to problems with Coulomb friction at the interface, in which case, the zones of stick and slip also remain self-similar with monotonically increasing indentation force.
See I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York (1980), §1.622.1.
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(2004). Frictionless Contact. In: Elasticity. Solid Mechanics and Its Applications, vol 107. Springer, Dordrecht. https://doi.org/10.1007/0-306-48395-5_26
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DOI: https://doi.org/10.1007/0-306-48395-5_26
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