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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 593))

Abstract

Contacts are classified into the fundamental types and their characteristics briefly explored. The formulation of incomplete contacts using a half-plane formulation is then developed, and used to obtain the plane solution for a Hertzian contact, while providing the framework for many other geometries. Williams’ solution for a sharp infinite elastic wedge is described in detail, and it is shown how this may be applied to advantage in understanding complete contacts and especially their near-edge properties. We then go back to look at incomplete contacts and analyse how they respond when there is interfacial friction present and they remain stationary, but a partial slip state evolves. The chapter concludes by reviewing the other possible types of contact.

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Notes

  1. 1.

    Dundurs (1969) showed that plane elastic problems composed of two bodies depend not on the obvious three dimensionless properties \(\nu _{1},\nu _{2}, E_{1}/E_{2}\) but, in fact, on only two quantities (\(\alpha ,\beta \)). Half-plane problems have a further reduced dependence on only the solitary quantity \(\beta .\)

  2. 2.

    Note that, in defining crack tip stress intensity factors, for historical reasons the stress intensity factors have an extra factor of \(\sqrt{2\pi }\) included in both Eq. (1.51) in the denominator, and in the right hand side of the definitions of stress intensity factor, Eqs. (1.52) and (1.53).

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Correspondence to David Hills .

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Hills, D., Andresen, H. (2020). Fundamentals of Elastic Contacts. In: Paggi, M., Hills, D. (eds) Modeling and Simulation of Tribological Problems in Technology. CISM International Centre for Mechanical Sciences, vol 593. Springer, Cham. https://doi.org/10.1007/978-3-030-20377-1_1

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  • DOI: https://doi.org/10.1007/978-3-030-20377-1_1

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