Displacement‐based and hybrid formulations of zero‐thickness mortar/interface elements for unmatched meshes, with application to fracture mechanics

Abstract

The present article develops two formulations of zero‐thickness mortar/interface finite elements for unmatched meshes, which are implemented in a unified theoretical framework. The first one is displacement‐based and may be considered a natural extension of the traditional zero‐thickness interface element to the case of unmatched meshes on each side of the discontinuity. The other one is hybrid, with an interpolation of stress tractions along the contact surface, which coexists with the standard displacement interpolations of the continuum surfaces in contact. The hybrid formulation shares some features with mortar formulations found in the literature of contact‐friction, and turns out fully equivalent to the displacement‐based in the particular case of matched nodes and uniform, linear elastic behavior. Flow chart diagrams for the numerical implementation are also presented and discussed, as well as some examples of application.