Comparative analysis of nonlinear buckling and postbuckling in shear-deformable sandwich composite toroidal shell segments with diverse auxetic cores and CNT-reinforced face sheets

This study, for the first time, analyzes and compares the influence of diverse auxetic cores on the buckling and postbuckling behavior of shear-deformable auxetic-core sandwich-structured toroidal shell segments (TSSs) with carbon nanotube (CNT)-reinforced face sheets supported by a Kerr-type elastic foundation and subjected to external pressure. The CNTs are embedded in a polymer matrix throughout the face sheet thickness, either uniformly (UD) or as functionally graded (FG) distributions. The metamaterial core features four types of recently developed auxetic designs: (1) a 3D augmented re-entrant cellular structure, (2) an arc-type auxetic design inspired by the traditional re-entrant honeycomb structure, (3) a bio-inspired butterfly-shaped auxetic structure, and (4) a star-shaped auxetic structure. The Kerr-type elastic foundation is modeled using a three-parameter configuration consisting of a central shear layer and two spring layers on the top and bottom surfaces. The governing equations for the TSSs are derived using Reddy's third-order shear deformation theory (TSDT) and incorporate von Kármán-type geometric nonlinearity. A three-term deflection solution under simply supported boundary conditions is employed, with the Galerkin method used to establish the nonlinear load–deflection relationship. The effectiveness of the proposed approach is validated through comparative analysis with existing literature, demonstrating excellent agreement with theoretical results. A comprehensive parametric analysis is conducted to identify the auxetic core that offers the best buckling and postbuckling performance of sandwich TSSs under varying relative densities of the auxetic core structures, geometric parameters of the TSSs, and Kerr-type elastic foundation properties.