Buckling and Postbuckling Analysis of Graphene Origami–Enabled Auxetic Metamaterial Sandwich Toroidal Shell Segments Subjected to Axial Compression

Due to the ongoing interest in novel negative Poisson ratio (NPR) materials, this study examines the buckling and postbuckling behavior of sandwich-structured composite toroidal shell segments (TSS) with graphene origami (GOri)–reinforced auxetic core and face sheets reinforced with carbon nanotubes (CNTs). These TSS are subjected to axial compression and surrounded by an elastic foundation. The CNTs are embedded in a polymer matrix with either a uniform distribution (UD) or a functionally graded (FG) distribution across the shell thickness. The nonlinear equilibrium equations of the longitudinally shallow shells are derived using von Kármán shell theory and Stein and McElman approximations, with the Winkler–Pasternak elastic foundation employed to model the shell–foundation interaction. A three-term solution for deflection under simply supported boundary conditions is utilized, and the Galerkin method is applied to establish the nonlinear load–deflection relationship. This relationship is subsequently used to determine buckling loads and postbuckling behavior. Numerical investigations focus on the impact of the GOri-enabled-core sandwich TSS, taking into account the CNT volume fraction, distribution types, geometrical parameters, and the presence of an elastic medium on their buckling and postbuckling performance.