This article is focused on the examination of the buckling properties of butterfly-shaped honeycomb (BSH) auxetic doubly curved nanoshells. First, higher-order shear deformation theory (HSDT) is applied, followed by nonlocal strain gradient theory (NSGT) and Hamilton’s method to derive the motion equations. Finally, Navier’s method is employed to analyze the buckling behavior of BSH nanoshells by solving these equations. The numerical results of this research are compared with previous works, and thus, the accuracy of the results is confirmed. Furthermore, a comprehensive analysis is conducted on how the nonlocal parameter, strain gradient length scale, curvature radius, and geometric dimensions of the butterfly-shaped auxetic structure influence the behavior of the BSH nanoshell.
HanDRenXZhangY, et al. Lightweight auxetic metamaterials: design and characteristic study. Compos Struct2022; 293: 115706.
5.
ZhangXYRenXZhangY, et al. A novel auxetic metamaterial with enhanced mechanical properties and tunable auxeticity. Thin-Walled Struct2022; 174: 109162.
6.
TheocarisPSStavroulakisGEPanagiotopoulosPD.Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach. Arch Appl Mech1997; 67: 274–286.
7.
MeenaKSingamneniS.Novel hybrid auxetic structures for improved in-plane mechanical properties via additive manufacturing. Mech Mater2021; 158: 103890.
8.
ZhangXYWangXYRenX, et al. A novel type of tubular structure with auxeticity both in radial direction and wall thickness. Thin-Walled Struct2021; 163: 107758.
9.
WangWDaiSZhaoW, et al. Reliability-based optimization of a novel negative Poisson's ratio door anti-collision beam under side impact. Thin-Walled Struct2020; 154: 106863.
10.
ZhangZTianRZhangX, et al. A novel butterfly-shaped auxetic structure with negative Poisson’s ratio and enhanced stiffness. J Mater Sci2021; 56: 14139–14156.
11.
KelkarPUKimHSChoK-H, et al. Cellular auxetic structures for mechanical metamaterials: a review. Sensors2020; 20: 3132.
12.
LiKZhangYHouY, et al. Mechanical properties of re-entrant anti-chiral auxetic metamaterial under the in-plane compression. Thin-Walled Struct2023; 184: 110465.
13.
GomesRAde OliveiraLAFranciscoMB, et al. Tubular auxetic structures: a review. Thin-Walled Struct2023; 188: 110850.
14.
NickabadiSSayarMAAlirezaeipourS, et al. Optimizing an auxetic metamaterial structure for enhanced mechanical energy absorption: design and performance evaluation under compressive and impact loading. J Sandwich Struct Mater2024; 26: 1129–1164.
15.
UstaFScarpaFTürkmenHS, et al. Multiphase lattice metamaterials with enhanced mechanical performance. Smart Mater Struct2021; 30: 025014.
16.
LiangYCDouJHBaiQS.Molecular dynamic simulation study of AFM single-wall carbon nanotube tip-surface interactions. Key Eng Mater2007; 339: 206–210.
17.
MehralianFTadi BeniYKarimi ZeverdejaniM.Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes. Physica B2017; 514: 61–69.
18.
YangFChongACMLamDCC, et al. Couple stress based strain gradient theory for elasticity. Int J Solids Struct2002; 39: 2731–2743.
19.
AifantisEC.Strain gradient interpretation of size effects. Fract Scale1999; 95: 299–314.
20.
LamDCCYangFChongACM, et al. Experiments and theory in strain gradient elasticity. J Mech Phys Solids2003; 51: 1477–1508.
21.
EringenAC.Linear theory of nonlocal elasticity and dispersion of plane waves. Int J Eng Sci1972; 10: 425–435.
22.
EringenACWegnerJL.Nonlocal continuum field theories. Appl Mech Rev2003; 56: B20–B22.
23.
HosseiniSRahmaniOBayatS.A new solution for dynamic response of FG nonlocal beam under moving harmonic load. Steel and Composite Structures, An International Journal2022; 43: 185–200.
24.
AfshariradFMousanezhadSBiglariH, et al. Molecular dynamics of axial interwall van der Waals force and mechanical vibration of double-walled carbon nanotubes. Mater Today Commun2021; 28: 102708.
25.
CongPHDucND.Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments. Thin-Walled Struct2021; 163: 107748.
26.
LiuXZhongYLiuR, et al. Buckling and post-buckling analysis of butterfly-shaped auxetic core sandwich plates based on variational asymptotic method. Thin-Walled Struct2023; 184: 110464.
27.
Phung-VanPNguyen-XuanHHungPT, et al. Nonlocal strain gradient analysis of honeycomb sandwich nanoscale plates. Thin-Walled Struct2024; 198: 111746.
28.
Van LieuPZenkourAMLuuGT. Static bending and buckling of FG sandwich nanobeams with auxetic honeycomb core. Eur J Mech A Solids2024; 103: 105181.
29.
DarvishiFRahmaniO.Calibration of nonlocal generalized helical beam model for free vibration analysis of coiled carbon nanotubes via molecular dynamics simulations. Mech Adv Mater Struct2023; 30: 1624–1648.
30.
QuangVDQuanTQTranP.Static buckling analysis and geometrical optimization of magneto-electro-elastic sandwich plate with auxetic honeycomb core. Thin-Walled Struct2022; 173: 108935.
31.
NtayeeshTJArefiM.Higher-order displacement, strain, and stress analyses of origami graphene auxetic metamaterial-reinforced cylindrical shell. Arch Civil Mech Eng2024; 24: 1–20.
32.
NosratiSRahmaniOHosseiniSA.Free vibration analysis of butterfly-shaped auxetic doubly curved nano-shells with nonlocal strain gradient theory. Thin-Walled Struct2025; 214: 113380.
33.
HongNT.Static and dynamic buckling analysis of two-layer shells include auxetic honeycomb core combined with laminated three-phase polymer/GNP/fiber surface resting on Kerr elastic medium in hygro-thermal environments. Mech Based Des Struct Mach2025; 53(1): 18–55.
34.
DarvishiFRahmaniOOstadrahimiA, et al. Molecular dynamics simulation of free transverse vibration behavior of single-walled coiled carbon nanotubes. Mech Adv Mater Struct2024; 31: 5028–5039.
35.
AlaviFKashmarizadKRahmaniO.From empirical to machine learning potentials: Unraveling the physical properties of grapheneplus—a novel half-auxetic 2D carbon nanosheet. Comput Mater Sci2025; 257: 113996.
36.
TabakASafaeiBMemarzadehA, et al. An extensive review of piezoelectric energy-harvesting structures utilizing auxetic materials. J Vib Eng Technol2024; 12: 3155–3192.
37.
RamezaniMJRahmaniO.Potential and applications of auxetic tubular: a review. Funct Compos Struct2024; 6: 012001.
38.
WangXFuT.Improvement of broadband low-frequency sound insulation of sandwich plates with negative Poisson's ratio butterfly-shaped auxetic cellular. Eng Anal Bound Elem2024; 166: 105852.
39.
AskesHAifantisEC.Gradient elasticity and flexural wave dispersion in carbon nanotubes. Phys Rev B2009; 80: 195412.
40.
TuPHVan KeTTraiVK, et al. An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading. Def Technol2024; 41: 159–180.
41.
TouratierM.An efficient standard plate theory. Int J Eng Sci1991; 29: 901–916.
42.
Cuong-LeTNguyenKDLeeJ, et al. A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells. Nanotechnol2021; 33: 065703.
