Abstract
As we noted in §16.4.1, Green and Zerna’s Solution F is ideally suited to the solution of frictionless contact problems for the half-space, since it identically satisfies the condition that the shear tractions be zero at the surface z = 0. In fact the surface tractions for this solution take the form whilst the surface displacements are from Table 16.2.
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Notes
Strictly this terminology is restricted to cases where the two regions A, Ā are connected. A special case where this condition is not satisfied is the indentation by an annular punch for which Ā has two unconnected regions—one inside the annulus and one outside. This would be referred to as a three-part problem.
See for example §12.5.3.
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 this argument see J.R. Barber, Determining the contact area in elastic contact problems, J.Strain Analysis, Vol. 9 (1974), 230–232.
Even then, the variational problem is far from trivial.
R.T. Shield, Load-displacement relations for elastic bodies, Z.angew.Math.Phyz. (ZAMP), Vol. 18 (1967), pp. 682–693.
D.A. Spence, An eigenvalue problem for elastic contact with finite friction, Proc. Camb. 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.
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© 1992 Springer Science+Business Media Dordrecht
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Barber, J.R. (1992). Frictionless Contact. In: Elasticity. Solid Mechanics and Its Applications, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2454-6_21
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