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.

塑性复合材料是一种新型的超材料，具有负泊松比（NPR）的有趣特征。当前的研究报道了面内NPR对由石墨烯增强金属基复合材料（GRMMC）制成的轴向加载圆柱壳的屈曲后响应的影响。GRMMC层压圆柱壳的每一层都可以改变其石墨烯的体积分数，从而获得功能梯度（FG）壳。GRMMC层具有随温度变化的材料特性，可以使用扩展的微机械Halpin-Tsai模型对其进行评估。GRMMC叠层壳的后屈曲控制方程基于雷迪三阶剪切变形理论。还包括vonKármán非线性应变-位移关系以及基础支撑和温度效应。通过使用奇异摄动技术结合两步摄动方法，可以对完美和不完善的FG-GRMMC叠层圆柱壳进行后屈曲，从而获得解析解。数值结果清楚地表明，面内NPR对GRMMC叠层圆柱壳在轴向压缩下的后屈曲响应和不完善敏感性有很大影响。