Functionally graded graphene origami-enabled auxetic metamaterial beams with tunable buckling and postbuckling resistance

•Buckling and postbuckling performances of shear deformation metamaterial beams are investigated.•Effects of graphene origami content, folding degree, and temperature are discussed in detail.•Symmetrical metamaterial distribution X offers significantly higher resistance against buckling and postbuckling.•Buckling and postbuckling responses FG-GOEAM beams are insensitive to temperature change. Auxetic metamaterials have emerged as novel advanced materials with unique physical and mechanical properties that conventional materials do not possess. This paper examines the buckling and postbuckling properties of functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) beams. The beam is comprised of multiple GOEAM layers with GOri content varying in layer-wise patterns to realize gradient-changing Poisson’s ratio and stiffness coefficient through the beam thickness. The material properties of each GOEAM layer are estimated by the genetic programming (GP)-assisted micromechanical models. The first-order shear deformation theory and von Kármán type nonlinearity are employed to derive the nonlinear governing equations that are numerically solved by the differential quadrature method (DQM). Numerical investigations are carried out with the main focus on the impacts of GOri content, distribution pattern, folding degree, and temperature on the buckling and postbuckling behaviors of FG metamaterial beams. The theoretical results show that GOri is capable of contributing to the formation of auxetic metal metamaterial, leading to the tunable bucking and postbuckling properties of FG beams, which sheds significant insights into the design of high-performance structures.