Materials having two or more constituents of different mechanical properties are often seen in engineering practice. These constituents are connected through their interfaces where the material displacements and tractions are most likely discontinuous, subjected to one, or more, of the five general interface conditions, i.e., perfectly bonded, dislocation-like, force-like, spring-like, and frictionless contact. This paper focus on the contact problem of a rigid sphere sliding on a layered half-space with a spring-like interface between the layer and the substrate. The frequency-domain analytical solutions for the elastic field caused by surface pressure and shear traction are derived. Three stiffness coefficients are introduced to reflect the relationship between tractions and the difference in displacements at both sides of the interface. Further, a sliding contact problem of a rigid sphere and a layered half-space with the spring-like interface is numerically investigated, and the effects of stiffness coefficients on the contact behaviors are explored. Finally, the two-layer model for a coated surface with an inner layer is compared to the spring-like model. When the inner layer is thin and soft, the pressures, as well as stresses, obtained by both models are similar to each other, and the two models are equivalent.
Wang, Z., Yu, H., & Wang, Q. (2017). Layer-substrate system with an imperfectly bonded interface: Spring-like condition. International Journal of Mechanical Sciences, 134, 315–335. https://doi.org/10.1016/j.ijmecsci.2017.10.028