The Sliding of a Rigid Indentor Over a Power Law Viscoelastic Halfspace
TEXAS A AND M UNIV COLLEGE STATION DEPT OF MATHEMATICS
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Closed form solutions are obtained for the problem of a rigid asperity sliding with Coulomb friction over a power law viscoelastic halfspace. 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. It is observed that for certain power law materials, singularities in the normal traction field occur even for the smooth parabolic indentor.