THE SLIDING OF A RIGID INDENTOR OVER A POWER - LAW VISCOELASTIC HALF-SPACE

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Abstract
Closed form solutions are obtained for the problem of a rigid asperity sliding with Coulomb friction over a power-law viscoelastic half-space. The dual integral equations relating the unknown normal traction under the contact interval (also unknown) to the unknown normal displacement outside the contact interval are solved by first reducing the system to a generalized Abel integral equation and then appealing to the theory of Riemann-Hilbert boundary-value problems. The physical quantities of interest (eg. the coefficient of sliding friction) are determined for the three canonical indentors: a parabolic punch, a wedge punch, and a flat punch. The analysis predicts singularities in the normal stress field for certain power-law materials even for the smooth parabolic indentor.

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