The isogeometric collocated contact surface approach

TL;DR

This paper introduces an isogeometric collocated contact surface (CCS) formulation that enforces frictionless contact constraints pointwise, achieving high accuracy and computational efficiency in contact analysis.

Contribution

The paper presents a novel CCS approach that combines collocated contact enforcement with standard Galerkin bulk treatment, improving accuracy and simplicity over existing methods.

Findings

Passes the contact patch test to machine precision.

Less oscillation issues on non-uniform meshes compared to collocation-based discretizations.

More efficient and easier to implement than integral contact methods.

Abstract

We propose a frictionless contact formulation for isogeometric analysis, which combines a collocated formulation for the contact surfaces with a standard Galerkin treatment of the bulk. We denote it as isogeometric Collocated Contact Surface (CCS) formulation. The approach is based on a simple pointwise enforcement of the contact constraints, performed in this study with the penalty method. Unlike pointwise (node-to-surface or point-to-surface) contact algorithms in the Galerkin framework, the CCS formulation passes the contact patch test to machine precision by naturally exploiting the favorable properties of isogeometric collocation. Compared with approaches where the discretization of both bulk and contact surfaces is based on collocation, the CCS approach does not need enhancements to remove oscillations for highly non-uniform meshes. With respect to integral contact approaches, the CCS algorithm is less expensive, easier to code and can be added to a pre-existing isogeometric analysis code with minimal effort. Numerical examples in both small and large deformations are investigated to compare the CCS approach with some available contact formulations and to demonstrate its accuracy.