Nonlinear bending analysis of matrix cracked functionally graded graphene origami-enabled auxetic metamaterial plates using the C⁰-HSDT meshless method

The auxetic metamaterials characterized by negative Poisson’s ratio (NPR) are attracting significant interest due to their extraordinary and captivating mechanical properties. This paper presents a meshless model based on the Improved Moving Kriging (IMK) interpolation to investigate the nonlinear bending of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterials (GOEAM) plates with matrix cracks. The model is based on the C 0 -higher order shear deformation theory ( C 0 -HSDT) framework with seven variables and incorporates the von-Karman nonlinearity. The material properties of FG-GOEAM plate are determined by a genetic programming (GP)-assisted micromechanics model, while the degraded stiffness of cracked layers is incorporated via a self-consistent micromechanics model. The convergence and effectiveness of the proposed method is examined by comparing it with existing literature results. Firstly, the convergence and validity of the method presented in this paper are verified through comparison with existing literature. Then, A comprehensive study is conducted to examine key parametric effects on the tunability of nonlinear bending deflection and normal stress in matrix-cracked FG-GOEAM plates. The results show that higher GOri content enhances the stiffness of the FG-GOEAM plate, leading to lower deflection, whereas increased GOri folding degree results in greater deflection. Additionally, the deflection and in-plane stress of the matrix-cracked FG-GOEAM plate are higher than those of the intact plate, while shear stress is lower, with these effects becoming more pronounced as crack density increases.