An Atlas of Extreme Properties in Cubic Symmetric Metamaterials

Abstract

Current research on three-dimensional metamaterial has largely focused on conventional strut, plate, and shell-based lattice designs. Although these designs offer several advantages, they possess inherent limitations that can restrict their performance in certain applications, motivating the exploration of alternative structural topologies. Here, we present a large-scale, symmetry guided framework for the generation and analysis of architected metamaterials based on all 36 cubic space groups. Using a voxel-based representation, we construct a database of approximately 1.95 million periodic unit cells spanning a broad range of relative densities and topological complexity. This dataset reveals a rich elastic property landscape shaped by crystallographic symmetry, including rare pentamode designs with high bulk to shear ratios such as $K/G \approx 166$ , isotropic-auxetic architectures with Poisson's ratio as low as $\nu=-0.76$, and structures achieving up to 93% of the Hashin-Shtrikman upper bound on stiffness. Complementing the dataset, we develop a three-dimensional convolutional neural network surrogate model trained and evaluated on the full database to predict strain-energy density values under uniaxial, shear, and hydrostatic loading. Together, this work establishes a comprehensive atlas of cubic symmetric metamaterials and provides a pre-trained model for the accelerated discovery and design of 3D architected materials with extreme mechanical properties.