Projection-based model reduction for contact problems

TL;DR

This paper presents a projection-based model reduction method for contact problems in nonlinear finite element analysis, utilizing non-negative matrix factorization and a greedy sampling algorithm to improve efficiency and robustness.

Contribution

It introduces a novel reduction approach combining non-negative matrix factorization and greedy sampling for contact problems, addressing a key challenge in nonlinear model reduction.

Findings

Effective reduction of contact models demonstrated on 2D examples

Robustness achieved across parameter variations

Significant computational efficiency gains shown

Abstract

To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for the reduction of nonlinear computational mechanics models, addressing the issue of contact remains a major hurdle. To this effect, this paper introduces a projection-based model reduction approach for both static and dynamic contact problems. It features the application of a non-negative matrix factorization scheme to the construction of a positive reduced-order basis for the contact forces, and a greedy sampling algorithm coupled with an error indicator for achieving robustness with respect to model parameter variations. The proposed approach is successfully demonstrated for the reduction of several two-dimensional, simple, but representative contact and self contact computational models.