Wallpaper Group-Based Mechanical Metamaterials: Dataset Including Mechanical Responses.

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Mechanics

Background:

• Mechanical metamaterials leverage pattern transformations via instabilities for diverse applications.
• Microstructure symmetries critically influence metamaterial behavior but are under-explored.
• Designing metamaterials is complex due to vast design spaces and machine learning data needs.

Purpose of the Study:

• To generate a comprehensive dataset of 2D microstructures and their mechanical responses.
• To investigate the relationship between microstructure symmetries and macroscopic mechanical properties.
• To provide data for developing and benchmarking machine learning models for metamaterial design.

Main Methods:

• Novel microstructure generation covering all 17 wallpaper symmetry groups using Bézier curves.
• Finite element-based computational homogenization to determine mechanical responses.
• Creation of a dataset with 1,020 unique geometries and 12,240 loading trajectories.

Main Results:

• A large-scale dataset linking 2D microstructure geometry, symmetry, and hyperelastic, finite-strain mechanical response.
• Inclusion of buckling phenomena in the mechanical response data.
• Data spans all 17 wallpaper symmetry groups, offering broad coverage.

Conclusions:

• The dataset facilitates the study of symmetry-property relationships in mechanical metamaterials.
• Enables development and validation of surrogate models for accelerated design.
• Supports research into symmetry-breaking and emergent behaviors during pattern transformations.