An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

TL;DR

This paper introduces an enriched finite element method that effectively handles contact and non-conforming mesh coupling problems without locking, ensuring displacement continuity and accurate traction transfer.

Contribution

The proposed formulation enriches finite element discretizations with generalized degrees of freedom, enabling locking-free contact and mesh coupling with stable and accurate results.

Findings

Ensures displacement continuity without locking in mesh coupling.

Transfers accurate contact tractions without stabilization.

Maintains stability with a simple diagonal preconditioner.

Abstract

We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multiple-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. The method's ability to ensure continuity of the displacement field -- without locking -- in mesh coupling problems, and to transfer fairly accurate tractions at contact interfaces -- without the need for contact stabilization -- is demonstrated by means of several examples. In addition, we show that the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.