Sparse approximations for contact mechanics

TL;DR

This paper introduces a dictionary-based sparse approximation method for contact mechanics that efficiently models contact pressure fields by inducing sparsity, overcoming limitations of traditional low-rank reduction techniques.

Contribution

The paper proposes a novel sparse approximation approach using a large dictionary of contact pressure trajectories for efficient and accurate contact mechanics modeling.

Findings

The method achieves high accuracy with reduced computational effort.

Sparsity induction improves model efficiency.

Limitations are discussed through numerical examples.

Abstract

Low-rank model order reduction strategies for contact mechanics show limited dimensionality reduction due to linear inseparability of contact pressure field. Therefore, a dictionary based strategy is explored for creating efficient models for frictionless non-adhesive contact. A large dictionary of contact pressure trajectories is generated using a high-fidelity finite element model, while approximating the online query with a small number of dictionary entries. This is achieved by inducing sparsity in the approximation. Accuracy, computational effort and limitations of such methods are demonstrated on few numerical examples.