The Hertz problem for a rigid spherical indenter on a viscoelastic half-space was studied by Lee and Radok [1] in which the radius a(t) of the contact area is a monotonically increasing function of time t. Later, Hunter [2] studied the rebound of a rigid sphere on a viscoelastic half-space so that the contact radius a(t) increases monotonically to a maximum and then decreases to zero monotonically. The contact problem in which a(t) increases for the second time and decreases again does not seem to have been studied; nor has the contact problem in which a(t) is nonzero initially and decreases monotonically been studied. In this paper, a method is introduced so that the contact problem can be solved for arbitrary a(t). The rigid indenter is assumed to be smooth and axisymmetric but otherwise arbitrary. The viscoelastic solutions are expressed in terms of the associated elastic solutions. A means for measuring the viscoelastic Poisson’s ratio is suggested.

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