Thin–Walled Structures 157 (2020) 107090 Available online 9 October 2020 0263-8231/© 2020 Elsevier Ltd. All rights reserved. Effect of negative poisson’s ratio on the axially compressed postbuckling behavior of FG-GRMMC laminated cylindrical panels on elastic foundations Hui-Shen Shen a, b, * , Y. Xiang c a School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China b School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China c School of Engineering, Western Sydney University, Locked Bag 1797, Penrith, NSW, 2751, Australia A R T I C L E INFO Keywords: Auxetic materials Functionally graded Temperature dependent Cylindrical panel Postbuckling ABSTRACT Auxetic materials are one of the metamaterials that have potential applications in many scientifc and engi- neering felds. In this paper, an investigation is presented on the postbuckling responses of axially loaded gra- phenereinforced metal matrix composite (GRMMC) laminated cylindrical panels with in-plane negative Poisson’s ratio (NPR). The panels are made of GRMMC laminates and rest on an elastic foundation in thermal environ- ments. The graphene volume fraction in GRMMC layer may vary across the panel thickness in order to achieve a piece-wise functionally graded (FG) pattern. The GRMMC layers have in-plane NPR and temperature dependent material properties. The governing differential equations for the GRMMC laminated cylindrical panels are formulated based on the Reddy’s third order shear deformation shell theory and are solved by using a singular perturbation technique along with a two-step perturbation approach. Numerical investigation is carried out to study the infuence of the in-plane NPR, the FG patterns, the thermal environmental conditions and the foun- dation stiffness on the postbuckling responses of the GRMMC laminated cylindrical panels under axial compressive load. The results reveal that the in-plane NPR can lead to a substantial change of the postbuckling behaviors of the GRMMC laminated cylindrical panels. 1. Introduction Researches on advanced materials have emerged to be the focus of many material scientists and engineers in recent years. One type of the advanced materials is the auxetic materials which exhibit negative Poisson’s ratios, i. e. when stretched the material becomes thicker and when compressed it becomes thinner. Comparing with conventional materials, auxetic mate- rials have enhanced performance in acoustic damping, energy absorption, indentation resistance and fracture resistance. Potential applications of such materials may be found in the felds of smart flters, sensors, medical devices and protective equipment [1–3]. Studies on creating fber reinforced composite (FRC) laminates with negative Poisson’s ratios (NPRs) can be found in open literature [4–8]. The out-of-plane NPR can be obtained for laminates when certain orientation angles and stacking sequence of the plies are applied. Re- searchers found that the range of the out-of-plane NPRs is from 0.5 [5], 1 [ 6] to more than 2 [7] for FRC laminates. It was also reported that a higher magnitude NPR can be achieved for carbon fber reinforced composite (CFRC) laminates with more severe anisotropy [8]. Due to the extraordinary material properties of carbon nanotubes (CNTs), a substantial amount of research work has been reported on carbon nanotube reinforced composites (CNTRCs) to achieve desirable material properties of the new nanocomposites. One of the distinctive characteristics of CNTRCs is that the high level of difference between the two in-plane Young’s moduli with their ratio being as large as 40 and it was reported that such material can exhibit auxetic material properties with large negative Poisson’s ratios [9]. CNTRCs in general cannot contain as high volume fraction of CNT reinforcement as that of fber reinforcement in FRCs due to issues relating to CNT dispersion and composite fabrication process etc. One approach to fully utilize CNT reinforcement is to apply the functionally graded (FG) concept [10] in CNTRC structures, as frst proposed by Shen [11], to enhance the me- chanical responses of the structures. To study the effect of out-of-plane NPR on structural behaviors, Shen and his co-authors [12–17] investi- gated the nonlinear bending and the large amplitude vibration responses of FG-CNTRC laminated structures for the frst time. They have identi- fed that the out-of-plane NPR has a moderate impact on the responses of the structures. However, no study can be found on the change of * Corresponding author. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail address: hsshen@sjtu.edu.cn (H.-S. Shen). Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: http://www.elsevier.com/locate/tws https://doi.org/10.1016/j.tws.2020.107090 Received 3 May 2020; Received in revised form 5 August 2020; Accepted 24 August 2020