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

arXiv: https://arxiv.org/abs/2112.14234 · HTML: https://mlsanity.com/paper/2112.14234/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)

## Abstract (arXiv)

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.