Assessing thermomechanical stability characteristics of shear deformable sandwich composite toroidal shells with bio-inspired auxetic core

This work investigates the thermomechanical stability response of bio-inspired auxetic-core, shear-deformable sandwich toroidal shell segments (TSSs) with carbon nanotube (CNT)-reinforced face sheets. The TSSs are subjected to external pressure and thermal fields, including a uniform temperature rise and linear or nonlinear gradients along the shell thickness, and are supported by a Kerr foundation. The core of the sandwich structure features an innovative auxetic metamaterial modeled after the geometry of a butterfly, known as a butterfly-shaped auxetic design. This proposed topological design offers greater stiffness than conventional re-entrant auxetic structures with a negative Poisson's ratio (NPR). The fundamental equations are established within the framework of Reddy's third-order shear deformation theory (TSDT), and the Galerkin method is employed to obtain the nonlinear postbuckling response of the sandwich shells. Comparison with prior studies verifies the accuracy of the proposed model. Numerical analyses reveal the influence of the butterfly-shaped auxetic core's geometric parameters, thermal conditions, and Kerr foundation properties on critical buckling loads and postbuckling curves. Results demonstrate the proposed auxetic core's superior stability to traditional re-entrant auxetic structures, providing valuable insights for designing lightweight metamaterial TSSs with NPR for advanced engineering applications.