Physics-Informed Neural Networks for Bending Analysis of Graphene Origami-Enabled Auxetic Metamaterial Beams Based on Modified Coupled Stress Theory

Investigating the deformation behavior of graphene-reinforced composite structures holds significant engineering implications, while the rapid advancement of machine learning has introduced new technical approaches to structural bending analysis. In this study, we investigate the mechanical bending behavior of graphene origami (GOri)-enabled auxetic metamaterial beams using a physics-informed neural network (PINN). GOri-enabled auxetic metamaterials represent an innovative composite system characterized by a negative Poisson’s ratio (NPR) and superior mechanical performance. Here, we propose a composite beam model incorporating the modified coupled stress theory (MCST) and employing the PINN method to solve higher-order bending governing equations. Compared to the analytical solution, the accuracy and effectiveness of the PINN framework as a meshless solver for higher-order partial differential equations are verified. The bending properties of metamaterial beams are studied by considering the mechanical properties and size effect of metamaterials. It was found that the length scale parameters, more graphene platelets, and a higher folding degree have the best reinforcement effect on composite beams. By systematically varying the GOri folding parameters and graphene content, we demonstrate the robustness of the PINN methodology in resolving microscale beam bending phenomena, particularly in capturing complex size-effect interactions.