The Contact Problem for Viscoelastic Bodies

The contact problem in viscoelasticity is one in which different types of boundary conditions are prescribed depending on whether boundary points inside or outside the region of contact are considered. Since, in general, the contact region varies with time, this lends to a problem which cannot be treated directly by application of the Laplace transform, which has formed the basis for most published viscoelastic stress-distribution solutions. It is shown that the solution of the viscoelastic counterpart of the Hertz problem in elasticity can, however, be deduced from the elastic solution. A particular example is presented, and the marked effect of viscoelastic behavior on the pressure distribution in the contact region is illustrated. The problem also illustrates the tentative nature of the method of approach and the need for a separate confirmation of the solution. The solution is presented for general linear viscoelastic operators and offers the possibility of determining these from a contact test.