Boussinesq problem of a Burgers viscoelastic layer on an elastic substrate

•Surface loading is applied on viscoelastic layer deposited on elastic substrate.•The Burgers model is used to this problem to obtain an analytical solution.•Perfect bonding and frictionless contact at interface are considered.•Creep deformation is always observed in viscoelastic layer.•Plastic deformation is most probable to occur at surface loading center.

Viscoelastic problem of normal stress acting on the surface of a viscoelastic layer on an elastic half-space is analyzed. The Burgers (four elements) model is used to describe the deformation behavior of the viscoelastic layer. Two limiting cases are considered for the contact conditions 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.