Viscoelastic inclusion I: Partial contact under Bi-directional loading

Abstract

The problem of a viscoelastic material with an infinite cylindrical cavity occupied by a cylinder of another viscoelastic material and subject to varying stresses at infinity, is considered in the non-inertial approximation. The case where a constant compressive stress is applied along one axis and a varying stress along the other, is solved in detail. A condition determining the contact region is given. This region depends on material parameters in a more complex way than in the elastic case. Integral equations for the pressure and gap functions are derived and numerically solved.¶Detailed numerical results are presented for materials modelled as standard linear solids. One result of interest is that during the unloading phase, the pressure distribution is quite different from the elastic circular shape. It becomes more like a uniform distribution with a sharp fall-off near the end of the contact region. For materials with large viscoelastic losses, there is a small peak near the edge of the interval and the maximum pressure is out at the edges rather than at the centre.