Boussinesq type solution for a viscoelastic thin film on an elastic substrate

Understanding the deformation of solids under the action of surface loading plays an important role in experimentally characterizing the mechanical behavior of materials. Considering the role of a viscoelastic layer in controlling the deformation of a bilayer structure, we analyze the problem of normal stress acting on the surface of a viscoelastic layer on an elastic half-space. The standard linear solid model is used to describe the deformation behavior of the viscoelastic layer. Two limiting cases are considered for the contact condition between the viscoelastic layer and the elastic substrate; one is perfect bonding, and the other is frictionless contact. Using the Hankel transform, analytical expressions of the displacement and stress components in the bilayer structure are derived. The numerical results illustrate the effect of the layer thickness and the mechanical properties of materials on the surface displacement at the center of the loading zone.