Reduced-order structure-property linkages for stochastic metamaterials (dataset)

Stochastic Metamaterial Unit Cells Dataset This dataset contains binary topologies of stochastic metamaterial unit cells and their corresponding effective elastic constant \( C_{11} \) normalized by the Young's modulus of solid regions \( E \). It is intended to support research on structure–property linkages, materials informatics, and machine learning applications. The dataset is associated with the publication: H. Danesh, M. Annamaraju, T. Brepols, S. Reese, & S.R. Kalidindi, Reduced-order structure-property linkages for stochastic metamaterials, Physical Review Materials 9 (2025) 075201. DOI: https://doi.org/10.1103/8zzt-4b7z In this work, the unit cell topologies were extracted from "Bastek & Kochamann (2023)" and solved for their normalized effective elastic constant \( C_{11}\) using FFT-based homogenization. The homogenization assumes an isotropic linear elastic material characterized by Young's modulus \( E = 1 .0 \) and Poisson's ratio \( \nu = 0.3 \) for solid regions. The \( C_{11} \) values can be rescaled for any desired Young's modulus \( E^* \) by simply multiplying the provided \( C_{11} \) values by \( E^* \): \( C_{11}^\text{scaled} = C_{11}^\text{reported} \cdot E^* \) Dataset Structure The data can be accessed in two formats: 1) structures_c11.npz structures: Numpy array of shape (53019, 96, 96), containing 53019 binary unit cells of 96 × 96 pixels (0 = void, 1 = solid). c11: Numpy array of shape (53019, ), containing the normalized effective elastic constant \( C_{11} \) for each unit cell. This file can be loaded using Python: import numpy as np data = np.load('structures_c11.npz') structures = data['structures'] # Binary structures: shape (53019, 96, 96) c11 = data['c11'] # Normalized effective elastic constants: shape (53019,) 2) png_csv.zip structures/: Folder containing 53,019 PNG images, each representing a binary unit cell of 96 × 96 pixels (white: void, black: solid). c11.csv: CSV file containing normalized effective elastic constant \( C_{11} \) for each unit cell. This format is provided for users who prefer accessing the data as images and a CSV file. Disclaimer This dataset is provided "as is" without any express or implied warranties. The user is solely responsible for any consequences resulting from its use. Dataset Origin The topologies of the metamaterial unit cells used in this work are based on the publicly available dataset from: J.H. Bastek & D.M. Kochmann, Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models: dataset and model checkpoints. ETHZ Research Collection (2023). https://doi.org/10.3929/ethz-b-000629716 J.H. Bastek & D.M. Kochmann, Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models. Nat Mach Intell 5, 1466–1475 (2023). https://doi.org/10.1038/s42256-023-00762-x The original dataset is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).