dataset-spinodoids-and-bones-elastic-stiffness

Dataset for the publication:

W. Deng, S. Kumar, A. Vallone, D.M. Kochmann, and J.R. Greer, "AI-Enabled Materials Design of Non-periodic 3D Architectures with Predictable Direction-dependent Elastic Properties", Advanced Materials, 2308149 (2024), DOI: https://doi.org/10.1002/adma.202308149.

File and data column descriptions

• Deng_et_al_spinodoid_dataset.csv: This file contains the homogenized anisotropic elastic stiffness of spinodoids; used for training and testing the machine learning models (ML). The ML code from Kumar et al., Npj Comput. Mater. 2020, 6 (DOI: 10.1038/s41524-020-0341-6) is used and which is available here: https://github.com/mmc-group/inverse-designed-spinodoids.

Columns	Description
volFrac	Spinodoid relative density or volume fraction $\rho$
thetaX	Spinodoid design parameter $\theta_1$
thetaY	Spinodoid design parameter $\theta_2$
thetaZ	Spinodoid design parameter $\theta_3$
stiffness$k$	Homogenized anisotropic stiffness component of the spinodoid corresponding to the design parameters $(\rho,\theta_1,\theta_2,\theta_3)$. Here, $k$ denotes zero-indexed serialized index of the 6x6 stiffness matrix ($C$) in Voigt notation. E.g., stiffness8 denotes $C_{23}$. Due to orthotropic symmetry and alignment of principal axes with coordinate system, only the 9 non-zero stiffness components are listed.

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• Deng_et_al_bones_dataset.csv: This file contains the homogenized anisotropic elastic stiffness of bone samples used for inverse design benchmark of the ML models. It also contains the spinodoid design parameters obtained from inverse design to match the bone samples and the corresponding homogenized anisotropic elastic stiffness of the spinodoids.

Columns	Description
name	Bone sample (see Deng_et_al_bone_image_data description for reference)
volFrac	Bone relative density or volume fraction
alpha_radians	Angle (in radians) of rotation about $x_3$ axis involved in obtaining orthotropic approximation of the bone sample
beta_radians	Angle (in radians) of rotation about $x_1$ axis involved in obtaining orthotropic approximation of the bone sample
gamma_radians	Angle (in radians) of rotation about $x_2$ axis involved in obtaining orthotropic approximation of the bone sample
C$k$	Homogenized anisotropic stiffness component of the bone sample. Here, $k$ denotes zero-indexed serialized index of the 6x6 stiffness matrix ($C$) in Voigt notation.
Corth$k$	Orthotropic approximation of the homogenized anisotropic stiffness component of the bone sample. Here, $k$ denotes zero-indexed serialized index of the 6x6 stiffness matrix ($C$) in Voigt notation.
contrast	Young's modulus of the base material: $E_s$ (arbitrary choice)
spin_volFrac	Spinodoid relative density or volume fraction $\rho$ (obtained from inverse design to match the bone stiffness)
spin_thetaX	Spinodoid design parameter $\theta_1$ (obtained from inverse design to match the bone stiffness)
spin_thetaY	Spinodoid design parameter $\theta_2$ (obtained from inverse design to match the bone stiffness)
spin_thetaZ	Spinodoid design parameter $\theta_3$ (obtained from inverse design to match the bone stiffness)
spin_Corth$k$	Homogenized anisotropic stiffness component of the inverse-designed spinodoid sample, in the same coordinate frame as the orthotropic approximation of bone stiffness.
spin_C$k$	Homogenized anisotropic stiffness component of the inverse-designed spinodoid sample, in the same coordinate frame as the original bone stiffness.
spin_Rinv$ij$	3D Rotation matrix to go from the coordinate frame of spin_Corth to that of spin_C. Here, $ij$ denotes the component $i^\text{th}$ row and $j^\text{th}$ column component of the 3x3 matrix.

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• Deng_et_al_bone_image_data: This folder contains the 3D image data of the bone samples.
  • Each bone sample is represented by a 100x100x100 grayscale matrix.
  • Each data is stored in .mat which can be parsed directly into the matrix form in MATLAB.
  • The samples were extracted from much larger micro-CT images of the database: Javad Hazrati-Marangalou (2013): Database of femur samples. Version 1. 4TU.ResearchData. Dataset. https://doi.org/10.4121/uuid:4ae59365-92f0-480b-a899-ade34bc84a00. Please also cite this reference as original source if you use the extracted image data from our dataset.
  • File nomenclature convention: XXXX_bY.mat denotes the Y-th small sample extracted from the original 3D image/FEM file FEM0XXXX by Javad Hazrati-Marangalou (2013). The numbering choice of Y is arbitrary.

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Citation

If you use this data, please cite the publication: W. Deng, S. Kumar, A. Vallone, D.M. Kochmann, and J.R. Greer, "AI-Enabled Materials Design of Non-periodic 3D Architectures with Predictable Direction-dependent Elastic Properties", Advanced Materials, 2308149 (2024), DOI: 10.1002/adma.202308149

Shield:

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.