A Machine learning approach for predicting orientation-dependent elastic properties of 2D materials

Abstract

Orientation-dependent mechanical properties, such as Young’s modulus (E), shear modulus (G), and Poisson’s ratio (ν), play a crucial role in characterizing the anisotropic behavior of two-dimensional (2D) materials. Conventionally, these properties are determined through tensorial transformations of second-order elastic stiffness tensors (C_ij) as a function of angle, followed by analysis of the resulting elastic surfaces to identify extrema (E_max, E_min, G_max, G_min, ν_max, ν_min). The ratio of E_max /E_min serves as a key indicator of elastic anisotropy, while the occurrence of negative ν_min identifies auxetic behavior. This work presents a machine learning approach, specifically employing a neural network, to directly predict these extrema from the elastic constants (C₁₁, C₁₂, C₂₂, C₆₆). A comprehensive dataset of over 6300 2D materials, extracted from the computational 2D materials database (C2DB), was used to train and validate the model. The developed model demonstrates exceptional predictive accuracy, exceeding 99 % for all predicted extrema, thereby bypassing the computationally intensive process of explicit tensorial transformations and orientation-dependent calculations. This efficient and accurate methodology enables rapid screening of 2D materials for specific mechanical properties, facilitating the identification of auxetic materials and the quantification of elastic anisotropy. This efficient approach enables the rapid screening of 2D materials for desired mechanical properties, facilitating the identification of auxetic materials and the quantification of elastic anisotropy. The developed methodology has the potential to accelerate materials discovery and design for a range of applications, including flexible electronics, mechanical metamaterials, and nano-scale devices.