Effect of negative Poisson's ratio on the postbuckling behavior of axially compressed FG-GRMMC laminated cylindrical shells surrounded by an elastic medium

Auxetic composites are one of novel metamaterials which exhibit an interesting feature of negative Poisson's ratio (NPR). The current study reports the impact of in-plane NPR on the postbuckling responses of axially loaded cylindrical shells made of graphene-reinforced metal matrix composite (GRMMC) layers. Each layer of a GRMMC laminated cylindrical shell can vary its graphene volume fraction so that a functionally graded (FG) shell is achieved. The GRMMC layers possess temperature-dependent material properties that can be evaluated using an extended micromechanical Halpin–Tsai model. The governing equations for the postbuckling of GRMMC laminated shells are based on the Reddy's third order shear deformation theory. The von Kármán nonlinear strain-displacement relationships together with the foundation support and temperature effects are also included. Analytical solutions are obtained by using a singular perturbation technique in associate with a two-step perturbation approach for the postbuckling of perfect and imperfect FG-GRMMC laminated cylindrical shells. Numerical results explicitly show that the in-plane NPR has a substantial effect on the postbuckling response and imperfection sensitivity of GRMMC laminated cylindrical shells under axial compression.