Abstract
This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson’s ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin–Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge–Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.
References
1.
Zhou
, H.
, Xu
, P.
, and Xie
, S.
, 2017
, “Composite Energy-Absorbing Structures Combining Thin-Walled Metal and Honeycomb Structures
,” Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit.
, 231
(4
), pp. 394
–405
. 2.
Olympio
, K. R.
, and Gandhi
, F.
, 2010
, “Flexible Skins for Morphing Aircraft Using Cellular Honeycomb Cores
,” J. Intell. Mater. Syst. Struct.
, 21
(17
), pp. 1719
–1735
. 3.
Wang
, Z.
, 2019
, “Recent Advances in Novel Metallic Honeycomb Structure
,” Compos. Part B Eng.
, 166
, pp. 731
–741
. 4.
Li
, X.
, Zhang
, P.
, Shiqiang
, L.
, Wang
, Z.
, and Wu
, G.
, 2018
, “Dynamic Response of Aluminum Honeycomb Sandwich Panels Under Foam Projectile Impact
,” Mech. Adv. Mater. Struct.
, 25
(8
), pp. 637
–646
. 5.
Bai
, Y.
, Yu
, K.
, Zhao
, J.
, and Zhao
, R.
, 2018
, “Experimental and Simulation Investigation of Temperature Effects on Modal Characteristics of Composite Honeycomb Structure
,” Compos. Struct.
, 201
, pp. 816
–827
. 6.
Zippo
, A.
, Ferrari
, G.
, Amabili
, M.
, Barbieri
, M.
, and Pellicano
, F.
, 2015
, “Active Vibration Control of a Composite Sandwich Plate
,” Compos. Struct.
, 128
, pp. 100
–114
. 7.
Amabili
, M.
, and Reddy
, J. N.
, 2021
, “Nonlinear Mechanics of Sandwich Plates: Layerwise Third-Order Thickness and Shear Deformation Theory
,” Compos. Struct.
, 278
, p. 114693
. 8.
Alijani
, F.
, Amabili
, M.
, Ferrari
, G.
, and D’Alessandro
, V.
, 2013
, “Nonlinear Vibrations of Laminated and Sandwich Rectangular Plates With Free Edges. Part 2: Experiments & Comparisons
,” Compos. Struct.
, 105
, pp. 437
–445
. 9.
Liu
, Y.
, Qin
, Z.
, and Chu
, F.
, 2022
, “Nonlinear Forced Vibrations of Rotating Cylindrical Shells Under Multi-harmonic Excitations in Thermal Environment
,” Nonlinear Dyn.
, 108
(4
), pp. 2977
–2991
. 10.
Liu
, Y.
, Zhu
, R.
, Qin
, Z.
, and Chu
, F.
, 2022
, “A Comprehensive Study on Vibration Characteristics of Corrugated Cylindrical Shells With Arbitrary Boundary Conditions
,” Eng. Struct.
, 269
, p. 114818
. 11.
Dai
, Q.
, and Liu
, Y.
, 2022
, “Dynamic Stability Analysis of Periodic Loaded Rotating Conical Shells Using Floquet Exponent Method
,” Mech. Based Des. Struct. Mach.
, pp. 1
–15
. 12.
Lakes
, R.
, 1987
, “Foam Structures With a Negative Poisson’s Ratio
,” Science (80-).
, 235
(4792
), pp. 1038
–1040
. 13.
Lim
, T.-C.
, 2015
, Auxetic Materials and Structures
, Springer
, New York
.14.
Yang
, L.
, Harrysson
, O.
, West
, H.
, and Cormier
, D.
, 2015
, “Mechanical Properties of 3D Re-Entrant Honeycomb Auxetic Structures Realized Via Additive Manufacturing
,” Int. J. Solids Struct.
, 69
, pp. 475
–490
. 15.
Qiao
, J.
, and Chen
, C. Q.
, 2015
, “Analyses on the In-Plane Impact Resistance of Auxetic Double Arrowhead Honeycombs
,” ASME J. Appl. Mech.
, 82
(5
), p. 051007
. 16.
Zhu
, X.
, Zhang
, J.
, Zhang
, W.
, and Chen
, J.
, 2019
, “Vibration Frequencies and Energies of an Auxetic Honeycomb Sandwich Plate
,” Mech. Adv. Mater. Struct.
, 26
(23
), pp. 1951
–1957
. 17.
Duc
, N. D.
, Seung-Eock
, K.
, Tuan
, N. D.
, Tran
, P.
, and Khoa
, N. D.
, 2017
, “New Approach to Study Nonlinear Dynamic Response and Vibration of Sandwich Composite Cylindrical Panels With Auxetic Honeycomb Core Layer
,” Aerosp. Sci. Technol.
, 70
, pp. 396
–404
. 18.
Li
, H.
, Li
, Z.
, Xiao
, Z.
, Xiong
, J.
, Wang
, X.
, Han
, Q.
, Zhou
, J.
, and Guan
, Z.
, 2022
, “Vibro-Impact Response of FRP Sandwich Plates With a Foam Core Reinforced by Chopped Fiber Rods
,” Compos. Part B Eng.
, 242
, p. 110077
. 19.
Nguyen
, N. V.
, Nguyen-Xuan
, H.
, Nguyen
, T. N.
, Kang
, J.
, and Lee
, J.
, 2021
, “A Comprehensive Analysis of Auxetic Honeycomb Sandwich Plates With Graphene Nanoplatelets Reinforcement
,” Compos. Struct.
, 259
, p. 113213
. 20.
Elamin
, M.
, Li
, B.
, and Tan
, K. T.
, 2021
, “Compression After Impact Performance of Carbon-Fiber Foam-Core Sandwich Composites in Low Temperature Arctic Conditions
,” Compos. Struct.
, 261
, p. 113568
. 21.
Hao
, Y. X.
, Zhou
, W. B.
, Zhang
, W.
, Yang
, S. W.
, and Cao
, Y. T.
, 2022
, “Dynamic Snap-Through of Bi-Stable Laminates With Simply Supported at Four Corners Under Impact Loads
,” Mech. Based Des. Struct. Mach.
, pp. 1
–20
. 22.
Chen
, S.
, Tan
, X.
, Hu
, J.
, Wang
, B.
, Wang
, L.
, Zou
, Y.
, and Wu
, L.
, 2022
, “Continuous Carbon Fiber Reinforced Composite Negative Stiffness Mechanical Metamaterial for Recoverable Energy Absorption
,” Compos. Struct.
, 288
, p. 115411
. 23.
Chen
, Y.
, Yang
, J.
, Peng
, J.
, Ji
, C.
, and Wang
, B.
, 2023
, “Low-Velocity Impact (LVI) and Post-Impact Fatigue Properties of GLARE Laminates With Holes
,” Int. J. Fatigue
, 167
, p. 107318
. 24.
Zhou
, X. Q.
, and Wang
, L.
, 2019
, “Low-Velocity Impact Response of Viscoelastic Material Filled FG Honeycomb Reinforced Laminate Plate in Hygrothermal Environments
,” Compos. Part B Eng.
, 165
, pp. 255
–271
. 25.
Zhang
, Y.
, Yan
, L.
, Zhang
, C.
, and Guo
, S.
, 2021
, “Low-Velocity Impact Response of Tube-Reinforced Honeycomb Sandwich Structure
,” Thin-Walled Struct.
, 158
, p. 107188
. 26.
He
, W.
, Yao
, L.
, Meng
, X.
, Sun
, G.
, Xie
, D.
, and Liu
, J.
, 2019
, “Effect of Structural Parameters on Low-Velocity Impact Behavior of Aluminum Honeycomb Sandwich Structures With CFRP Face Sheets
,” Thin-Walled Struct.
, 137
, pp. 411
–432
. 27.
Li
, Q. Q.
, He
, Z. C.
, Li
, E.
, and Cheng
, A. G.
, 2019
, “Improved Impact Responses of a Honeycomb Sandwich Panel Structure With Internal Resonators
,” Eng. Optim.
, 52
(5
), pp. 731
–752
.28.
Sun
, G.
, Huo
, X.
, Wang
, H.
, Hazell
, P. J.
, and Li
, Q.
, 2021
, “On the Structural Parameters of Honeycomb-Core Sandwich Panels Against Low-Velocity Impact
,” Compos. Part B Eng.
, 216
, p. 108881
. 29.
Zhang
, J.
, Yuan
, H.
, Li
, J.
, Meng
, J.
, and Huang
, W.
, 2022
, “Dynamic Response of Multilayer Curved Aluminum Honeycomb Sandwich Beams Under Low-Velocity Impact
,” Thin-Walled Struct.
, 177
, p. 109446
. 30.
Zhang
, J.
, Zhu
, X.
, Yang
, X.
, and Zhang
, W.
, 2019
, “Transient Nonlinear Responses of an Auxetic Honeycomb Sandwich Plate Under Impact Loads
,” Int. J. Impact Eng.
, 134
, p. 103383
. 31.
Wang
, H.
, Lu
, Z.
, Yang
, Z.
, and Li
, X.
, 2019
, “A Novel Re-Entrant Auxetic Honeycomb With Enhanced in-Plane Impact Resistance
,” Compos. Struct.
, 208
, pp. 758
–770
. 32.
Katunin
, A.
, Pawlak
, S.
, Wronkowicz-Katunin
, A.
, and Tutajewicz
, D.
, 2020
, “Damage Progression in Fibre Reinforced Polymer Composites Subjected to Low-Velocity Repeated Impact Loading
,” Compos. Struct.
, 252
, p. 112735
. 33.
Gan
, J.
, Li
, F.
, Li
, K.
, Li
, E.
, and Li
, B.
, 2023
, “Dynamic Failure of 3D Printed Negative-Stiffness Meta-Sandwich Structures Under Repeated Impact Loadings
,” Compos. Sci. Technol.
, 234
, p. 109928
. 34.
Zhang
, J.
, Zhu
, Y.
, Li
, K.
, Yuan
, H.
, Du
, J.
, and Qin
, Q.
, 2022
, “Dynamic Response of Sandwich Plates With GLARE Face-Sheets and Honeycomb Core Under Metal Foam Projectile Impact: Experimental and Numerical Investigations
,” Int. J. Impact Eng.
, 164
, p. 104201
. 35.
Liao
, B.
, Zhou
, J.
, Li
, Y.
, Wang
, P.
, Xi
, L.
, Gao
, R.
, Bo
, K.
, and Fang
, D.
, 2020
, “Damage Accumulation Mechanism of Composite Laminates Subjected to Repeated Low Velocity Impacts
,” Int. J. Mech. Sci.
, 182
, p. 105783
. 36.
Dai
, X.
, Yuan
, T.
, Zu
, Z.
, Ye
, H.
, Cheng
, X.
, and Yang
, F.
, 2020
, “Experimental Investigation on the Response and Residual Compressive Property of Honeycomb Sandwich Structures Under Single and Repeated Low Velocity Impacts
,” Mater. Today Commun.
, 25
, p. 101309
. 37.
Zhou
, J.
, Liu
, B.
, and Wang
, S.
, 2022
, “Finite Element Analysis on Impact Response and Damage Mechanism of Composite Laminates Under Single and Repeated Low-Velocity Impact
,” Aerosp. Sci. Technol.
, 129
, p. 107810
. 38.
Balcı
, O.
, Çoban
, O.
, Bora
, MÖ
, Akagündüz
, E.
, and Yalçin
, E. B.
, 2017
, “Experimental Investigation of Single and Repeated Impacts for Repaired Honeycomb Sandwich Structures
,” Mater. Sci. Eng. A
, 682
, pp. 23
–30
. 39.
Acar Yavuz
, G.
, Gören Kıral
, B.
, Hızarcı
, B.
, and Kıral
, Z.
, 2022
, “Low-Velocity Single and Repeated Impact Behavior of 3D Printed Honeycomb Cellular Panels
,” Mater. Test.
, 64
(10
), pp. 1420
–1436
. 40.
Abo Sabah
, S.H.
, Kueh
, A.B.H.
, and Al-Fasih
, M.Y.
, 2018
, “Bio-Inspired vs. Conventional Sandwich Beams: A Low-Velocity Repeated Impact Behavior Exploration
,” Constr. Build. Mater.
, 169
, pp. 193
–204
. 41.
Gibson
, L. J.
, 2003
, “Cellular Solids
,” Mrs Bull.
, 28
(4
), pp. 270
–274
. 42.
Feng
, C.
, Kitipornchai
, S.
, and Yang
, J.
, 2017
, “Nonlinear Bending of Polymer Nanocomposite Beams Reinforced With Non-Uniformly Distributed Graphene Platelets (GPLs)
,” Compos. Part B Eng.
, 110
, pp. 132
–140
. 43.
De Villoria
, R. G.
, and Miravete
, A.
, 2007
, “Mechanical Model to Evaluate the Effect of the Dispersion in Nanocomposites
,” Acta Mater.
, 55
(9
), pp. 3025
–3031
. 44.
Abrate
, S.
, 1998
, Impact on Composite Structures
, Cambridge University Press
, Cambridge
.45.
Crook
, A. W.
, 1952
, “A Study of Some Impacts Between Metal Bodies by a Piezo-Electric Method
,” Proc. R. Soc. London. Ser. A. Math. Phys. Sci.
, 212
(1110
), pp. 377
–390
.46.
Sun
, C. T.
, and Chen
, J. K.
, 1985
, “On the Impact of Initially Stressed Composite Laminates
,” J. Compos. Mater.
, 19
(6
), pp. 490
–504
. 47.
Reddy
, J. N.
, 2006
, Theory and Analysis of Elastic Plates and Shells
, CRC Press
, Boca Raton, FL
.48.
Amabili
, M.
, 2018
, Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
, Cambridge University Press
, Cambridge, UK
.49.
Liu
, Y.
, Qin
, Z.
, and Chu
, F.
, 2021
, “Nonlinear Forced Vibrations of Functionally Graded Piezoelectric Cylindrical Shells Under Electric-Thermo-Mechanical Loads
,” Int. J. Mech. Sci.
, 201
, p. 106474
. 50.
Amabili
, M.
, Sarkar
, A.
, and Païdoussis
, M. P.
, 2006
, “Chaotic Vibrations of Circular Cylindrical Shells: Galerkin Versus Reduced-Order Models Via the Proper Orthogonal Decomposition Method
,” J. Sound Vib.
, 290
(3
), pp. 736
–762
. 51.
Liu
, Y.
, Qin
, Z.
, and Chu
, F.
, 2021
, “Nonlinear Forced Vibrations of FGM Sandwich Cylindrical Shells With Porosities on an Elastic Substrate
,” Nonlinear Dyn.
, 104
(2
), pp. 1007
–1021
. 52.
Liu
, Y.
, Qin
, Z.
, and Chu
, F.
, 2022
, “Investigation of Magneto-Electro-Thermo-Mechanical Loads on Nonlinear Forced Vibrations of Composite Cylindrical Shells
,” Commun. Nonlinear Sci. Numer. Simul.
, 107
, p. 106146
. 53.
Cash
, J. R.
, and Karp
, A. H.
, 1990
, “A Variable Order Runge-Kutta Method for Initial Value Problems With Rapidly Varying Right-Hand Sides
,” ACM Trans. Math. Softw.
, 16
(3
), pp. 201
–222
. 54.
Zhang
, Y.-W.
, and She
, G.-L.
, 2023
, “Nonlinear Low-Velocity Impact Response of Graphene Platelet-Reinforced Metal Foam Cylindrical Shells Under Axial Motion With Geometrical Imperfection
,” Nonlinear Dyn.
, 111
(7
), pp. 6317
–6334
. 55.
Bayat
, M. R.
, Rahmani
, O.
, and Mosavi Mashhadi
, M.
, 2018
, “Nonlinear Low-Velocity Impact Analysis of Functionally Graded Nanotube-Reinforced Composite Cylindrical Shells in Thermal Environments
,” Polym. Compos.
, 39
(3
), pp. 730
–745
. 56.
Wang
, Z.-X.
, Xu
, J.
, and Qiao
, P.
, 2014
, “Nonlinear Low-Velocity Impact Analysis of Temperature-Dependent Nanotube-Reinforced Composite Plates
,” Compos. Struct.
, 108
, pp. 423
–434
. 57.
Liu
, Y.
, Hu
, W.
, Zhu
, R.
, Safaei
, B.
, Qin
, Z.
, and Chu
, F.
, 2022
, “Dynamic Responses of Corrugated Cylindrical Shells Subjected to Nonlinear Low-Velocity Impact
,” Aerosp. Sci. Technol.
, 121
, p. 107321
. Copyright © 2023 by ASME
You do not currently have access to this content.
