The viscoelastic contact problem is extended to cover general linear materials and arbitrary quadratic surfaces of the bodies in contact. Use of integral operator constitutive relations permits solution by comparison with a known integral identity in potential theory, as used by Hertz in the original elastic solution. Examples are given for the case of indentation of a viscoelastic half-space by a rigid spherical indenter and the case of contact between two spheres with different material properties.

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