Surface Green's functions for an anisotropic viscoelastic half-plane and their application to contact problems

In this paper, the elastic-like surface Green's functions for an anisotropic viscoelastic half-plane are derived using the time-stepping method. Using the elastic-like surface Green's functions as the core analytical solutions, we develop semi-analytical models (SAMs) and apply them to solve two different contact problems with anisotropic viscoelastic materials. As new modeling approaches, the SAMs developed here can provide fast and efficient approaches to solving contact problems. These methods enable us to consider contact problems with generally anisotropic viscoelastic solids, in which the contact surface is frictional and either smooth or rough, and the applied loads and boundaries can be time-variant. The correctness of the derived surface Green's functions is demonstrated by comparing the numerical results obtained by SAMs and those achieved from the analytical solutions or boundary element methods. Using the obtained numerical results, the impacts of time step size, anisotropy, frictional coefficient, roughness, and applied loads on the contact responses are further analyzed and discussed.