This work proposes a new approach to describe 2D frictional contact problems based on the use of coupling finite elements (CFEs) and a combined contact/friction damage constitutive model. This technique is able to establish the interaction between non-matching meshes, representing different subdomains (bodies) of a problem, which share common boundaries. The formulation is developed within a framework considering elastic bodies, small deformations and static loading conditions. Initially, the bodies are discretized in finite elements in a totally independent way. Then, CFEs are inserted to enforce the contact constraints in the context of penalty methods. As the CFEs share nodes from both sides of the non-matching meshes, an appropriate constitutive model can be easily defined to describe the interaction between the bodies on the contact interface based on the concept of a relative displacement. The proposed constitutive model is able to describe the frictional slippage and separation between the bodies. This constitutive model is integrated using an implicit–explicit scheme to avoid numerical convergence problems. The insertion of CFEs does not introduce any additional degree of freedom to the problem and these elements are introduced into the standard finite element mesh in a pre-processing stage to avoid pre-processing tasks during the analysis. The same framework is applied to deal with overlapping and non-overlapping meshes and its implementation in conventional FE programs is quite simple without drastic modifications. Five numerical analyses are performed and the results demonstrated that the strategy developed is able to represent the interaction between bodies, coherently and accurately.

这项工作提出了一种基于耦合有限元 (CFE) 和组合接触/摩擦损伤本构模型来描述二维摩擦接触问题的新方法。这种技术能够建立非匹配网格之间的交互，代表一个问题的不同子域（主体），它们共享公共边界。该公式是在考虑弹性体、小变形和静态载荷条件的框架内开发的。最初，物体以完全独立的方式在有限元中离散化。然后，插入 CFE 以在惩罚方法的上下文中强制执行接触约束。由于 CFE 共享来自非匹配网格两侧的节点，基于相对位移的概念，可以很容易地定义一个适当的本构模型来描述接触界面上的物体之间的相互作用。所提出的本构模型能够描述物体之间的摩擦滑动和分离。该本构模型使用隐式-显式方案进行集成，以避免数值收敛问题。CFE 的插入不会为问题引入任何额外的自由度，并且这些元素在预处理阶段被引入到标准有限元网格中，以避免分析过程中的预处理任务。相同的框架用于处理重叠和非重叠网格，它在传统 FE 程序中的实现非常简单，无需大刀阔斧的修改。