Inference of Substructured Reduced-Order Models for Dynamic Contact from Contact-free Simulations

TL;DR

This paper introduces a novel operator-inference-based reduction method for contact problems that uses contact-free simulation data, incorporating substructuring and constraints to accurately model contact dynamics.

Contribution

It presents a new reduction approach for contact problems that leverages dual systems and substructuring, enabling efficient modeling from contact-free simulation snapshots.

Findings

Effective reduction of 3D finite element contact models

Enforcement of matrix properties improves model accuracy

Validated on multiple complex finite element models

Abstract

In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system, where the corresponding Lagrange multipliers represent the contact pressure. The Craig-Bampton-like substructuring method is incorporated into the inference process to provide the reduced system matrices and the coupling of the contact and interior nodes. The maximum possible set of contact nodes must be known a priori. Characteristic properties of the inferred matrices, such as symmetry and positive definiteness, are enforced by appending additional constraints to the underlying least-squares problem. The resulting dual system, which forms a linear complementarity problem, is well-defined and can be effectively solved using methods such as Lemke's algorithm. The performance of the proposed method is validated on three-dimensional finite element models.