A data-driven framework for structure-property correlation in ordered and disordered cellular metamaterials

Extracting the relation between microstructural features and resulting material properties is essential for advancing our fundamental knowledge on the mechanics of cellular metamaterials and to enable the design of novel material systems. Here, we present a unified framework that not only allows the prediction of macroscopic properties but, more importantly, also reveals their connection to key morphological characteristics, as identified by the integration of machine-learning models and interpretability algorithms. We establish the complex manner in which strut orientation can be critical in determining effective stiffness for certain microstructures and highlight cellular metamaterials with counterintuitive material behavior. We further provide a refined version of Maxwell's criteria regarding the rigidity of frame structures and their connection to cellular metamaterials. By examining the shear moduli of these metamaterials, the mean cell compactness emerges as a key morphological feature. The generality of the proposed framework allows its extension to broader classes of architected materials as well as different properties of interest.