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.

中文翻译：

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各向异性粘弹性半平面的表面格林函数及其在接触问题中的应用


本文利用时间步进方法推导了各向异性粘弹性半平面的类弹性表面格林函数。使用类弹性表面格林函数作为核心解析解，我们开发了半解析模型（SAM）并将其应用于解决各向异性粘弹性材料的两个不同接触问题。作为新的建模方法，这里开发的 SAM 可以提供快速有效的方法来解决接触问题。这些方法使我们能够考虑一般各向异性粘弹性固体的接触问题，其中接触表面是摩擦的，光滑或粗糙，并且施加的载荷和边界可以随时间变化。通过比较 SAM 获得的数值结果与解析解或边界元方法获得的数值结果，证明了导出的表面格林函数的正确性。利用获得的数值结果，进一步分析和讨论了时间步长、各向异性、摩擦系数、粗糙度和施加载荷对接触响应的影响。