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The Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts. It is found that the Hertzian results are valid at sufficiently high loads, but at lower loads the effective pressure distribution is much lower and extends much further than for smooth surfaces. The relevance to the physical-contact theory of friction and electric contact is considered.
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Greenwood et al. (1967) studied this question.
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