大多数对于表面粗糙度摩擦行为的研究，以Greenwood和Williamson的粗糙表面模型（GW模型）为基础。一个粗糙体接触对通常被简化为简单的几何形状，如半球体或者圆柱体等。经过这样的简化处理，粗糙体的柔度往往被忽略。当表面比较粗糙，或者粗糙体的长细比较大时，粗糙体的柔度不能忽略。本文建立了考虑粗糙体柔度的接触模型，研究了接触过程接触力的演变以及功能损耗的机理。以尖端接触和非尖端接触两种接触形式分类，分别讨论了基体柔度对接触过程的贡献。

根据粗糙体柔度的不同，结合梁的变形规律，本文建立了两种梁理论接触模型。本文的主要研究工作及结论如下：

考虑到接触区局部的应力集中效应，建立了尖端接触梁理论模型。以Hertz压力分布分析接触区的局部变形，以梁的变形理论分析基体变形，耦合尖端局部变形和基体变形作为整体结构的接触响应。当基体柔度较小时，建立考虑剪切的Timoshenko梁理论尖端接触模型。当基体柔度较大时，结合梁的大变形原理，建立大挠度变形梁接触理论模型。经过与数值模拟结果的对比验证，分别得到了理论解的适用范围。研究发现：1)相比于不考虑基体柔度的纯弹性接触模型，滑动接触过程接触力呈反对称变化的情况，考虑了基体柔度的纯弹性接触模型的接触力呈非对称变化。2)随着粗糙体柔度的增加，结构趋向单方向的挠度变形，并发生结构失稳的现象。这种失稳现象是导致接触力反对称的原因，同时，接触力反对称将导致滑动接触过程存在摩擦损耗。

对于细长杆与障碍物的接触，非尖端接触成为主要的接触形式。根据梁的大变形原理和接触边界约束条件，建立大挠度变形梁理论接触模型。基于不同的运动模式，分析了接触过程作用力的变化以及能量分配的规律。讨论了不同梁长情况下，细长结构与障碍物接触行为的区别。研究发现：1) 细长杆与障碍物间发生接触分离的原因有两个：当初始梁长小于保持结构稳定的临界梁长时，物体间以“脱落”方式分离；当初始梁长大于结构保持稳定的临界梁长时，物体间以“滑落”方式分离。2)发生滑动分离的根本原因是，作用在细长杆上的力超过了维持结构稳定的力的临界值。

Most studies on the frictional behavior of rough surface are based on Greenwood and Williamson's model (GW model for short). The contact asperities are usually simplified to a shape such as a hemisphere or a cylinder. After such a simplification, the compliance of the asperity is often ignored. In this work, a contact model considering the compliance of the asperities was established, and the evolution of contact force and the mechanism of energy loss during contact were studied. The contribution of the substrate compliance to the contact process was discussed separately in the form of tip contact and non-tip contact.

According to the different compliance of the asperities, combined with the deformation law of the beam, we established two theoretical contact models. The main research methods and conclusions of this work are as follows:

Considering the effect of the local stress concentration in the contact area, a contact model of the tip contact with beam theory was proposed. The local deformation in the contact area was analyzed by Hertz pressure distribution, and the substrate deformation was analyzed by beam theory. The combination of the tip local deformation and substrate deformation was used as the contact response. When the asperity compliance is small, a contact model based on the Timoshenko beam model considering shear effect is established. When the asperity compliance is ​​large, the large deflection theory of the beam was applied to the contact model. After comparison with the finite element method, the applicable scope of the theoretical solution was obtained. The study found that: 1) As the asperity compliance increases, the revolution of the contact force will change from antisymmetric to asymmetric. 2) As the asperity compliance increases, the deflection of the structure tends to deform unidirectionally and the structure becomes unstable. This instability phenomenon leads to the formation of asymmetric contact force. At the same time, the asymmetric contact force will cause energy loss in the sliding contact process.

Non-tip contact is the primary contact form for the contact of the slender rod with an obstacle. In conjunction with the principle of large deflection of the beam and the constraint condition of the contact boundary, the theoretical contact model of large deflection beam is established. Based on different motion patterns, the changes of force in the contact process and the law of energy distribution were analyzed. The difference between the contact behavior of the slender structure and the obstacle with different presupposed beam lengths was discussed. The findings of this study include the following: 1) There are two ways for the contact detachment between the slender rod and obstacles. When the predefined beam length is less than the critical beam length to maintain the structural stability, the objects are detached in the way of "pull off". When the predefined beam length is more than the critical beam length to maintain the structural stability, the objects are detached in the way of "slip off". 2) The fundamental reason for the occurrence of “slip off” is that the force acting on the slender bar exceeds the critical value of the force that maintains the stability of the structure.