Wallpaper Group-Based Mechanical Metamaterials and their Mechanical Responses

This repository contains a dataset of geometries of potential mechanical metamaterials and their mechanical response, as described in our paper 'Wallpaper Group-Based Mechanical Metamaterials: Dataset Including Mechanical Responses', https://www.nature.com/articles/s41597-025-06150-x#citeas.

More specifically, a large dataset of 2D microstructures and their macroscopic mechanical responses in the hyperelastic, finite-strain regime including buckling. The geometries of the microstructures are generated using a novel method, which covers all 17 wallpaper symmetry groups and features a rich parametric space, as the microstructural geometries are described using Bézier curves. The mechanical responses are obtained through computational homogenization utilizing finite element simulations. The dataset includes 1020 distinct geometries, each subjected to 12 loading trajectories, totaling 12,240 trajectories. 

Our dataset offers a solid foundation for training and benchmarking surrogate models that aim to analyze the relationship between symmetries and material properties, investigating symmetry-breaking during pattern transformations, and potentially revealing emergent behavior in mechanical metamaterials.

The Python code used to generate the geometries is available at https://github.com/FHendriks11/wallpaper_microstructures, and the MATLAB code used for the finite element simulations is available at https://github.com/FHendriks11/mechmetamat_homogenization.

v2: updated README.md

v3: removed missed cases of contact

v4: replaced trajectories that ended in an error with converged trajectories

v5: replaced the one last trajectory that ended in an error with converged trajectory. Fixed time steps that were in the wrong order. Fixed one case where there was a mistake in the periodicity of the mesh. Updated README.md. 'contains_bifurcation' now contains False entry for trajectories with zero time steps for consistency with all other quantities.