This work investigates a three-dimensional size-dependent frictional contact problem of a rigid spherical punch sliding on an elastic half-space. The size-dependent material behaviors are governed by the couple stress theory, and the corresponding frequency response functions, which include two additional length-related elastic parameters, are obtained. Based on the conjugate gradient method and the discrete convolution-fast Fourier transform algorithm, a semi-analytical model is established to predict the frictional size-dependent contact behaviors and then the detailed parameter analysis is performed. The transverse effects of the couple stress, which are induced due to the considerations of the two additional elastic parameters in couple stress theory, are investigated in the contact problems for the first time. And the dependences of the size-dependent contact behavior on the coupling effects of the friction and the two additional elastic parameters are presented.

中文翻译：

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耦合应力弹性框架内的三维摩擦接触

这项工作研究了刚性球形冲头在弹性半空间上滑动的三维尺寸相关摩擦接触问题。与尺寸相关的材料行为由耦合应力理论控制，并获得相应的频率响应函数，其中包括两个附加的与长度相关的弹性参数。基于共轭梯度法和离散卷积快速傅里叶变换算法，建立半解析模型来预测摩擦尺寸相关的接触行为，然后进行详细的参数分析。首次在接触问题中研究了由于考虑力偶应力理论中的两个附加弹性参数而引起的力偶应力的横向效应。并提出了尺寸相关的接触行为对摩擦耦合效应和两个附加弹性参数的依赖性。