Computational modeling of 2D frictional contact problems based on the use of coupling finite elements and combined contact/friction damage constitutive model

Abstract

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.