This paper proposes an efficient contact model for a viscoelastic layered half-space where coating and substrate have different creep functions (i.e. different viscoelastic behaviours). The problem is formulated in three dimensions for an imposed pressure and shear field. The influence coefficients are calculated with the Papkovich-Neuber potentials and computation performed using Discrete Convolution and Fast Fourier Transform (DC-FFT) algorithms. From there, an elastic/viscoelastic correspondence is applied to move the elastic solution to a viscoelastic one. The Generalized Maxwell viscoelastic model is used and presented in the form of Prony series. A validation is performed using not only results within the literature but also by comparison with a finite element analysis. Next, a parametric study is done to analyse the influence of different parameters such as the elastic modulus ratio, the relaxation time ratio, the coating thickness or the rolling velocity. The model allows the analysis of the transient regime for which most of the known models struggle. It allows also to calculate 3D stresses and so to extract the stresses at the interface between the coating and the substrate so one can estimate the risk of failure such as delamination.

本文为粘弹性的分层半空间提出了一种有效的接触模型，该模型的涂层和基底具有不同的蠕变功能（即，不同的粘弹性行为）。对于施加的压力和剪切场，从三个维度来阐述问题。利用Papkovich-Neuber势计算影响系数，并使用离散卷积和快速傅里叶变换（DC-FFT）算法执行计算。从那里开始，应用弹性/粘弹性对应关系，将弹性溶液移动到粘弹性溶液。使用广义Maxwell粘弹性模型，并以Prony系列的形式表示。不仅使用文献中的结果，而且通过与有限元分析进行比较来进行验证。下一个，进行了参数研究，以分析不同参数的影响，例如弹性模量比，松弛时间比，涂层厚度或轧制速度。该模型允许分析大多数已知模型都难以解决的瞬态状态。它也可以计算3D应力，因此可以提取涂层与基材之间界面的应力，因此可以估算出诸如分层等失效风险。