Abstract Functionally graded (FG) graphene origami (GOri)‐enabled auxetic metamaterials (FG‐GOEAM) have attracted much attention due to their excellent negative Poisson's ratio (NPR) properties. At present, there is still a lack of research on the deflection deformation and instability of FG‐GOEAM plates. To fill this gap, the bending and buckling behaviors of FG‐GOEAM plates are systematically investigated for the first time in this study by using the three‐variable simplified plate theory (TVSPT), which successfully establishes the coupling relationship between the characteristic parameters of FG metamaterials and the displacement distribution of the plate structure in the thickness direction by introducing the parametric factors related to the elastic modulus of the material and the Poisson's ratio. The study examines FG‐GOEAM plates supported by an arbitrarily distributed Kerr elastic foundation and determines their locations and areas through accurate mathematical integration based on the TVSPT framework. The governing equations were derived by three‐dimensional elasticity theory and the static equilibrium principle, and the central deflection and critical buckling load of the plates under different boundary conditions were solved by the Galerkin's method. The results show that the FG metamaterial exhibits a pronounced NPR behavior with the increase of the GOri mass fraction. When GOri is enriched near the surface and its folding degree is reduced, the stiffness of the plate can be significantly enhanced. The numerical results of this work are expected to provide a theoretical foundation for the structural optimization and innovative design of FG‐GOEAM plates.
Li et al. (Tue,) studied this question.