[Paper Review] Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operators

Hanxun Jin, Enrui Zhang+4 more|arXiv (Cornell University)|Nov 23, 2023

Polymer composites and self-healing8 citations

TL;DR

The paper introduces a DeepONet-based SciML framework to learn the microstructure–nonlinear mechanical response of stochastic architected metamaterials from sparse in situ data and demonstrates inverse design of microstructures to achieve target stress–strain curves.

ABSTRACT

Machine learning (ML) is emerging as a transformative tool for the design of architected materials, offering properties that far surpass those achievable through lab-based trial-and-error methods. However, a major challenge in current inverse design strategies is their reliance on extensive computational and/or experimental datasets, which becomes particularly problematic for designing micro-scale stochastic architected materials that exhibit nonlinear mechanical behaviors. Here, we introduce a new end-to-end scientific ML framework, leveraging deep neural operators (DeepONet), to directly learn the relationship between the complete microstructure and mechanical response of architected metamaterials from sparse but high-quality in situ experimental data. The approach facilitates the inverse design of structures tailored to specific nonlinear mechanical behaviors. Results obtained from spinodal microstructures, printed using two-photon lithography, reveal that the prediction error for mechanical responses is within a range of 5 - 10%. Our work underscores that by employing neural operators with advanced micro-mechanics experimental techniques, the design of complex micro-architected materials with desired properties becomes feasible, even in scenarios constrained by data scarcity. Our work marks a significant advancement in the field of materials-by-design, potentially heralding a new era in the discovery and development of next-generation metamaterials with unparalleled mechanical characteristics derived directly from experimental insights.

Motivation & Objective

• Motivate the need for data-efficient inverse design of micro-architected metamaterials with nonlinear behavior.
• Propose an end-to-end SciML framework using DeepONet to map microstructure to nonlinear mechanical response.
• Incorporate symmetry-aware architecture to leverage inherent microstructure invariances.
• Demonstrate forward prediction accuracy on unseen microstructures using sparse experimental data.
• Showcase an inverse design workflow validated by experimental microstructure fabrication and testing.

Proposed method

• Use DeepONet to learn the operator mapping from microstructure cross-sections to full stress–strain curves under loading/unloading.
• Preprocess 3D microstructures into 2D cross-sections for the branch net.
• Incorporate an equivariance-preserving unit to enforce cross-section permutation invariance and directional permutation covariance.
• Train on sparse in situ SEM micro-compression data from spinodal microstructures and augmented microstructure datasets.
• Predict stress for given strain and loading step by dot-product of branch and trunk outputs, minimizing MSE with experimental curves.
• Apply a simplified indirect inverse design by using DeepONet as forward solver to optimize designs toward target curves.

Experimental results

Research questions

• RQ1 Can a neural operator learn the nonlinear, history-dependent stress–strain response of spinodal microstructures from sparse experimental data?
• RQ2 How well can the trained operator predict mechanical responses of unseen microarchitectures?
• RQ3 Can the framework be used for inverse design to achieve target isotropic or anisotropic mechanical behaviors?
• RQ4 What is the impact of incorporating symmetry (equivariance) on predictive accuracy and data efficiency?

Key findings

• DeepONet achieves 5-10% prediction error for mechanical responses on unseen microstructures.
• For unseen microstructures, predictions of stresses, energy absorption, ultimate stress, and stiffness yield R^2 > 0.96 and R^2 for stiffness = 0.90.
• Inverse design cases show target isotropic/aniso stress–strain curves with experimental validation: Case I isotropic MSE 1.07% (average in 3 directions) and experimental error 3.14%.
• Case II shows MSE 1.25% with experimental error 6.0%.
• Case III shows MSE 3.87% with experimental error 7.61%.
• Case IV shows directional MSEs of 7.99% and 2.73% (directions 2 and 3) and higher error in direction 1 (25.2%), attributed to buckling imperfections.