We conducted molecular statics simulations to investigate the negative Poisson's ratio (auxetic behavior) of periodic porous graphene structures based on the rotating rigid unit mechanism. To obtain a negative Poisson's ratio, simple voids were periodically introduced into graphene. We showed that the Poisson's ratio of the designed graphene structure is strongly dependent on the aspect ratio of the voids, and it can approach the theoretical limit of À1.0. More importantly, the graphene periodic structure maintains its auxetic behavior even under large strains (e $ 0.20). Hence, it can be employed in a wide range of applications requiring structures that can endure large deformation. In addition, we found that the key factor in the auxeticity of the investigated structures is the deformation occurring at the void tips.

We utilized molecular statics (MS) simulations to investigate the auxeticity of single layer black phosphorus (SLBP). Our simulation results show that the SLBP has a negative in‐plane Poisson's ratio in the zigzag direction when the applied strain along the armchair direction exceeds 0.018. We show that the interplay between bond stretching and bond rotating modes determines the in‐plane Poisson's ratio behavior. While the bond stretching mode always tends to increase the in‐plane auxeticity, the bond rotating mode might increase or decrease the in‐plane auxeticity. Furthermore, we show that graphite also exhibits an in‐plane negative Poisson's ratio at finite strains due to a similar mechanism.

A self-folding approach inspired by the origami technique is developed to form complex three-dimensional graphene structures using pattern-based surface functionalization.

The Poisson's ratio of two-dimensional materials such as graphene can be tailored by surface hydrogenation. The density and distribution of hydrogenation may significantly affect the Poisson's ratio of the graphene structure. Therefore, optimization of the distribution of hydrogenation is useful to achieve the structure with a targeted Poisson's ratio. For this purpose, we developed an inverse design algorithm based on machine learning using the XGBoost method to reveal the relationship between the Poisson's ratio and distribution of hydrogenation. Based on this relationship, we can optimize the hydrogenated graphene structure to have a low Poisson's ratio. Instead of performing molecular dynamic simulations for all possible structures, we could find the optimal structures using the search algorithm and save significant computational resources. This algorithm could successfully discover structures with low Poisson's ratios around −0.5 after only 1600 simulations in a large design space of approximately 5.2 × 10 6 possible configurations. Moreover, the optimal structures were found to exhibit excellent flexibility under compression of around −65% without failure and can be used in many applications such as flexible strain sensors. Our results demonstrate the applicability of machine learning to the efficient development of new metamaterials with desired properties.