An Efficient Model Order Reduction Scheme for Dynamic Contact in Linear Elasticity

TL;DR

This paper introduces a computationally efficient model order reduction method for dynamic contact problems in linear elasticity, utilizing the Linear Complementarity Programming approach and an Arnoldi process to simplify calculations while accurately satisfying contact constraints.

Contribution

It presents a novel reduction scheme based on LCP and Arnoldi methods, improving efficiency over traditional augmented Lagrangian approaches in contact problems.

Findings

Significant reduction in computational effort for contact problems.

Effective satisfaction of contact constraints after reduction.

Enhanced performance using Craig-Bampton extension.

Abstract

The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the Linear Complementarity Programming (LCP) method as basic methodology. It has the advantage of resulting in the much smaller dual problem that is associated with the governing variational principle and that turns out to be beneficial for the model order reduction. Since the shape of the contact zone depends strongly on the acting outer forces, the LCP for the Lagrange multipliers has to be solved in each time step. The model order reduction scheme, on the other hand, is applied to the large linear system for the displacements and computed in advance by means of an Arnoldi process. In terms of computational effort the reduction scheme is very appealing because the contact constraints are fully satisfied while the reduction acts only on the displacements. As an extension of our approach, we furthermore take up the idea of the Craig-Bampton method in order to distinguish between interior nodes and the nodes in the contact zone. A careful performance analysis closes the paper.