FRICTIONAL CONTACT WITH TRANSVERSE SHEAR

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Abstract
The problem considered is that of a rigid plane indentor pressed into a region −1P, with an overall shear force Q also acting, Q being less than ηP in magnitude, where η is the coefficient of Coulomb friction and the ratio Q/ηP is constant during the deformation. A solution satisfying the frictional constraints is obtained exhibiting an unsymmetrical region of adhesion (a, b) surrounded by regions (−1, a) and (b, 1) in which slip of opposite sign takes place. As the ratio Q/η;P increases from −1 to 1, the points a, b move from coincidence at x=+1 to coincidence at x=−1. The problem is first solved in a model form in which the pressure distribution is treated as independent of the shear (the Mindlin approximation); it is then shown that the full coupled problem can also be mapped into the symmetrical coupled problem treated by the author in a previous paper (1). A new asymptotic solution to this latter problem is obtained by use of the Wiener-Hopf technique in section 5.

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