Reduced-order structure-property linkages for stochastic metamaterials

TL;DR

This paper develops a computational framework combining principal component analysis, FFT-based homogenization, and Gaussian process regression to efficiently model the structure-property relationships of stochastic metamaterials, significantly reducing data requirements.

Contribution

It introduces a reduced-order modeling approach that captures complex structure-property linkages in stochastic metamaterials with minimal data, enabling efficient design and analysis.

Findings

High-dimensional data can be effectively reduced to low-dimensional features.

Surrogate models achieve accurate predictions with less than 1% of the original dataset.

Uncertainty-based active learning reduces data needs while maintaining robustness.

Abstract

The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective mechanical properties is critical for the efficient design and performance evaluation of such metamaterials. However, physics-based simulations of metamaterial unit cells across the entire design space are computationally expensive, necessitating a materials informatics framework to efficiently capture complex structure-property relationships. In this work, principal component analysis of 2-point correlation functions is performed to extract the salient features from a large dataset of randomly generated 2D metamaterials. Physics-based simulations are performed using a fast Fourier transform (FFT)-based homogenization approach to efficiently compute the homogenized effective elastic stiffness across the extensive unit cell designs. Subsequently, Gaussian process regression is used to generate reduced-order surrogates, mapping unit cell designs to their homogenized effective elastic constant. It is demonstrated that the adopted workflow enables a high-value low-dimensional representation of the voluminous stochastic metamaterial dataset, facilitating the construction of robust structure-property maps. Finally, an uncertainty-based active learning framework is utilized to train a surrogate model with a significantly smaller number of data points compared to the original full dataset. It is shown that a dataset as small as $0.61\%$ of the entire dataset is sufficient to generate accurate and robust structure-property maps.