2,285
Views
25
CrossRef citations to date
0
Altmetric
Original Articles

A review on the energy absorption response and structural applications of auxetic structures

, , , , &
Pages 5823-5842 | Received 03 Apr 2021, Accepted 05 Aug 2021, Published online: 12 Oct 2021

References

  • K. Evans and A. Alderson, Auxetic materials: Functional materials and structures from lateral thinking, Adv. Mater., vol. 12, no. 9, pp. 617–628, 2000. DOI: 10.1002/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3.
  • B. Ellul, M. Muscat, and J. N. Grima, On the efect of the Poisson’s ratio (positive and negative) on the stability of pressure vessel heads, Phys. stat. sol. (b)), vol. 246, no. 9, pp. 2025–2032, 2009. DOI: 10.1002/pssb.200982033.
  • M. Stavric and A. Wiltsche, Geometrical elaboration of auxetic structures, Nexus Netw. J. ., vol. 21, no. 1, pp. 79–90, 2019. DOI: 10.1007/s00004-019-00428-5.
  • G. N. Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel, Poisson's ratio and modern materials, Nature Mater., vol. 10, no. 11, pp. 823–837, 2011. DOI: 10.1038/nmat3134.
  • L. Francesconi, M. Taylor, K. Bertoldi, and A. Baldi, Static and modal analysis of low porosity thin metallic auxetic structures using speckle interferometry and digital image correlation, Exp. Mech. ., vol. 58, no. 2, pp. 283–300, 2018. DOI: 10.1007/s11340-017-0345-4.
  • D. Xiao, Z. Dong, Y. Li, W. Wu, and D. Fang, Compression behavior of the graded metallic auxetic reentrant honeycomb: experiment and finite element analysis, Mater. Sci. Eng.: A, vol. 758, pp. 163–171, 2019. DOI: 10.1016/j.msea.2019.04.116.
  • R. Lakes, Foam structures with a negative Poisson’s ratio, Science, vol. 235, no. 4792, pp. 1038–1040, 1987. DOI: 10.1126/science.235.4792.1038.
  • R. F. Almgren, An isotropic three-dimensional structure with Poisson’s ratio=-1, J. Elast., vol. 15, pp. 427–430, 1985. DOI: 10.1007/BF00042531.
  • I. G. Masters and K. E. Evans, Models for the elastic deformation of honeycombs, Compos. Struct., vol. 35, no. 4, pp. 403–422, 1996. DOI: 10.1016/S0263-8223(96)00054-2.
  • J. N. Grima and K. E. Evans, Auxetic behavior from rotating squares, J. Mater. Sci. Lett., vol. 19, no. 17, pp. 1563–1565, 2000. DOI: 10.1023/A:1006781224002.
  • J. N. Grima, A. Alderson, and K. E. Evans, Negative Poisson’s Ratios from rotating rectangles, Cmst, vol. 10, no. 2, pp. 137–145, 2004. DOI: 10.12921/cmst.2004.10.02.137-145.
  • M. Taylor, L. Francesconi, M. Gerendás, A. Shanian, C. Carson, and K. Bertoldi , Low porosity metallic periodic structures with negative Poisson's ratio, Adv. Mater., vol. 26, no. 15, pp. 2365–2370, 2014. DOI: 10.1002/adma.201304464.
  • D. Prall and R. Lakes, Properties of a chiral honeycomb with a Poisson’s ratio of –1, Int. J. Mech. Sci., vol. 39, no. 3, pp. 305–314, 1997. DOI: 10.1016/j.jpeds.2009.04.058.
  • S. Shan, S. H. Kang, Z. Zhao, L. Fang, and K. Bertoldi, Design of planar isotropic negative Poisson’s ratio structures, Extrem. Mech. Lett., vol. 4, pp. 96–102, 2015. DOI: 10.1016/j.eml.2015.05.002.
  • A. Alderson, and K. E. Evans, Microstructural modelling of auxetic microporous polymers, J. Mater. Sci., vol. 30, no. 13, pp. 3319–3332, 1995. DOI: 10.1007/BF00349875.
  • J. F. Clarke, R. A. Duckett, P. J. Hine, I. J. Hutchinson, and I. M. Ward, Negative Poisson’s ratios in angle-ply laminates: theory and experiment, Composites., vol. 25, no. 9, pp. 863–868, 1994. DOI: 10.1016/0010-4361(94)90027-2.
  • P. Michelis and V. Spitas, Numerical and experimental analysis of a triangular auxetic core made of CFR-PEEK using the directionally reinforced integrated single-yarn (DIRIS) architecture, Compos. Sci. Technol., vol. 70, no. 7, pp. 1064–1071, 2010. DOI: 10.1016/j.compscitech.2010.01.013.
  • R. S. Lakes, Negative-Poisson's-ratio materials: auxetic solids, Annu. Rev. Mater. Res., vol. 47, no. 1, pp. 63–81, 2017. DOI: 10.1146/annurev-matsci-070616-124118.
  • L. Jiang and H. Hu, Finite element modeling of multilayer orthogonal auxetic composites under low-velocity impact, Materials, vol. 10, no. 8, pp. 908, 2017. DOI: 10.3390/ma10080908.
  • L. Zhou, L. Jiang, and H. Hu, Auxetic composites made of 3D textile structure and polyurethane foam, Phys. Status Solidi B., vol. 253, no. 7, pp. 1331–1341, 2016. DOI: 10.1002/pssb.201552768.
  • J. Gao, M. Xiao, L. Gao, J. Yan, and W. Yan, Isogeometric topology optimization for computational design of re-entrant and chiral auxetic composites, Comput. Methods Appl. Mech. Eng., vol. 362, pp. 112876, 2020. DOI: 10.1016/j.cma.2020.112876.
  • R. Johnston, and Z. Kazancı, Analysis of additively manufactured (3D printed) dual-material auxetic structures under compression, Addit. Manuf., vol. 38, pp. 101783, 2021. [. DOI: 10.1016/j.addma.2020.101783.
  • M. Ouisse, M. Collet, and F. Scarpa, A piezo-shunted kirigami auxetic lattice for adaptive elastic wave filtering, Smart Mater. Struct., vol. 25, no. 11, pp. 115016, 2016. DOI: 10.1088/0964-1726/25/11/115016.
  • V. C. Vinay and D. M. Varma, Fabrication and testing of auxetic foams for rehabilitation applications, J. Indian Inst. Sci., pp. 1–8, 2019.
  • O. Duncan, T. Shepherd, C. Moroney, L. Foster, P. D. Venkatraman, K. Winwood, … and A. Alderson, Review of auxetic materials for sports applications: Expanding options in comfort and protection, Appl. Sci., vol. 8, no. 6, pp. 941, 2018. DOI: 10.3390/app8060941.
  • R. Gatt, L. Mizzi, J. I. Azzopardi, K. M. Azzopardi, D. Attard, A. Casha, J. Briffa, and J. N. Grima, Hierarchical auxetic mechanical metamaterials, Sci. Rep. 5., vol. 246, no. 9, pp. 2025–2032, 2015. DOI: 10.1002/pssb.200982033.
  • M.N. Ali, J.J.C. Busfield, and I.U. Rehman, Auxetic oesophageal stents: structure and mechanical properties. J. Mater. Sci: Mater Med., vol. 25, pp. 527–553, 2014. DOI: 10.1007/s10856-013-5067-2.
  • T.W. Tan, G. Douglas, T. Bond, and S. Phani, Compliance and longitudinal strain of cardiovascular stents: infuence of cell geometry, J. Med. Dev., vol. 5, no. 4, pp. 041002, 2011. DOI: 10.1115/1.4005226).
  • S. J. Linforth, 2020. Auxetic Armour System for Protection Against Soil Blast Loading (Doctoral dissertation). The University of Melbourne.
  • O. Duncan, L. Foster, T. Senior, A. Alderson, and T. Allen, Quasi-static characterisation and impact testing of auxetic foam for sports safety applications, Smart Mater. Struct., vol. 25, no. 5, pp. 054014, 2016. DOI: 10.1088/0964-1726/25/5/054014.
  • N. Novak, M. Vesenjak, and Z. Ren, Auxetic cellular materials - a review, SV-Jme, vol. 62, no. 9, pp. 485–493, 2016. DOI: 10.5545/sv-jme.2016.3656.
  • D. Tomažinčič, B. Nečemer, M. Vesenjak, and J. Klemenc, Low‐cycle fatigue life of thin‐plate auxetic cellular structures made from aluminium alloy 7075‐T651, Fat. Fract. Eng. Mater. Struct., vol. 42, no. 5, pp. 1022–1036, 2019. DOI: 10.1111/ffe.12966.
  • K. E. Evans and K. L. Alderson, Auxetic materials: the positive side of being negative, Eng. Sci. Educ. J., vol. 9, no. 4, pp. 148–154, 2000. DOI: 10.1049/esej:20000402.
  • K. L. Alderson, A. P. Pickles, P. J. Neale, and K. E. Evans, Auxetic polyethylene: the effect of a negative Poisson's ratio on hardness, Acta Metall. Mater., vol. 42, no. 7, pp. 2261–2266, 1994. DOI: 10.1016/0956-7151(94)90304-2.
  • F. Scarpa, L. G. Ciffo, and J. R. Yates, Dynamic properties of high structural integrity auxetic open cell foam, Smart Mater. Struct., vol. 13, no. 1, pp. 49–56, 2004. DOI: 10.1088/0964-1726/13/1/006.
  • R. S. Lakes, and K. Elms, Indentability of conventional and negative Poisson's ratio foams, J. Compos. Mater., vol. 27, no. 12, pp. 1193–1202, 1993. DOI: 10.1177/002199839302701203.
  • C. Lira, F. Scarpa, and R. Rajasekaran, A gradient cellular core for aeroengine fan blades based on auxetic configurations, J. Intell. Mater. Syst. Struct., vol. 22, no. 9, pp. 907–917, 2011. DOI: 10.1177/1045389X11414226.
  • L. White, Auxetic foam set for use in smart filters and wound dressings, Urethanes Technol. Int., vol. 26, no. 4, pp. 34–36, 2009.
  • N. Gupta, and K. M. Gupta, 2005. Metamaterial and auxetic hybrid composite antennas. In IEEE International Workshop on Antenna Technology: small Antennas and Novel Metamaterials, 2005 (IWAT 2005), pp. 414–417. IEEE. DOI: 10.1109/IWAT.2005.1461105.
  • C. Yang, H. D. Vora, and Y. B. Chang, Evaluation of auxetic polymeric structures for use in protective pads, ASME 2016 International Mechanical Engineering Congress and Exposition, Am. Soc. Mech. Eng. 2016, pp. V009T12A066–V009T12A066.
  • P. U. Kelkar, H. S. Kim, K. H. Cho, J. Y. Kwak, C. Y. Kang, and H. C. Song, Cellular auxetic structures for mechanical metamaterials: a review, Sensors, vol. 20, no. 11, pp. 3132, 2020. DOI: 10.3390/s20113132.
  • C. Huang and L. Chen, Negative Poisson’s ratio in modern functional materials, Adv. Mater. ., vol. 28, no. 37, pp. 8079–8096, 2016. DOI: 10.1002/adma.201601363.
  • Z. Qin, G. Qin, and M. Hu, Origin of anisotropic negative Poisson's ratio in graphene, Nanoscale., vol. 10, no. 22, pp. 10365–10370, 2018. DOI: 10.1039/C8NR00696B.
  • T. Zahra, and M. Dhanasekar, Characterisation of cementitious polymer mortar–Auxetic foam composites, Constr. Build. Mater., vol. 147, pp. 143–159, 2017. DOI: 10.1016/j.conbuildmat.2017.04.151.
  • C. Yang, H. D. Vora, and Y. B. Chang, 2016. Application of auxetic polymeric structures for body protection. In: Smart Materials, Adaptive Structures and Intelligent Systems, Vol. 50480, p. V001T01A018. American Society of Mechanical Engineers. DOI: 10.1115/SMASIS2016-9208.
  • X. Ren, J. H. Shen, A. Ghaedizadeh, H. Q. Tian, and M. Xie, 2016. Numerical simulations of 3D metallic auxetic metamaterials in both compression and tension. In: Applied Mechanics and Materials, Vol. 846, pp. 565–570. Trans Tech Publications Ltd. DOI: 10.4028/www.scientific.net/AMM.846.565.
  • T. Li, F. Liu, and L. Wang, Enhancing indentation and impact resistance in auxetic composite materials, Compos. B: Eng., vol. 198, pp. 108229, 2020. DOI: 10.1016/j.compositesb.2020.108229.
  • A. D. Lantada, A. de Blas Romero, M. Schwentenwein, C. Jellinek, and J. Homa, Lithography-based ceramic manufacture (LCM) of auxetic structures: present capabilities and challenges, Smart Mater. Struct., vol. 25, no. 5, pp. 054015, 2016. DOI: 10.1088/0964-1726/25/5/054015.
  • J. S. Hu, B. L. Wang, J. E. Li, and K. F. Wang, Thermal shock resistance behavior of auxetic ceramic honeycombs with a central crack or an edge crack, Ceram. Int., vol. 46, no. 8, pp. 11835–11845, 2020. DOI: 10.1016/j.ceramint.2020.01.218.
  • K. E. Evans, M. A. Nkansah, I. J. Hutchinson, and S. C. Rogers, Molecular network design, Nature., vol. 353, no. 6340, pp. 124–124, 1991. DOI: 10.1038/353124a0.
  • W. Voigt, Lehrbuch Der Kristallphysik, Vieweg + Teubner Verlag, Wiesbaden, 1966.
  • C. Lees, J. F. V. Vincent, and J. E. Hillerton, Poisson’s ratio in skin, Biomed Mater Eng., vol. 1, no. 1, pp. 19–23, 1991. DOI: 10.3233/BME-1991-1104.
  • Y. T. Yao, K. L. Alderson, and A. Alderson, Modeling of negative Poisson’s ratio (auxetic) crystalline cellulose I β, Cellulose., vol. 23, no. 6, pp. 3429–3448, 2016. DOI: 10.1007/s10570-016-1069-9.
  • T. Allen, T. Hewage, C. Newton‐Mann, W. Wang, O. Duncan, and A. Alderson, Fabrication of auxetic foam sheets for sports applications, Phys. Status Solidi B. ., vol. 254, no. 12, pp. 1700596, 2017. DOI: 10.1002/pssb.201700596.
  • S. L. Zhang, Y. C. Lai, X. He, R. Liu, Y. Zi, and Z. L. Wang, Auxetic foam‐based contact‐mode triboelectric nanogenerator with highly sensitive self‐powered strain sensing capabilities to monitor human body movement, Adv. Funct. Mater., vol. 27, no. 25, pp. 1606695, 2017. DOI: 10.1002/adfm.201606695.
  • F. Najarian, R. Alipour, M. S. Rad, A. F. Nejad, and A. Razavykia, Multi-objective optimization of converting process of auxetic foam using three different statistical methods, Measurement, vol. 119, pp. 108–116, 2018. DOI: 10.1016/j.measurement.2018.01.064.
  • M. J. Khoshgoftar and H. Abbaszadeh, Experimental and finite element analysis of the effect of geometrical parameters on the mechanical behavior of auxetic cellular structure under static load, J. Strain Anal. Eng. Design, V., vol. 56, n. no. 3, pp. 131–138, 2021. DOI: 10.1177/0309324720957573.
  • K. Meena and S. Singamneni, Novel hybrid auxetic structures for improved in-plane mechanical properties via additive manufacturing, Mech. Mater., vol. 158, pp. 103890, 2021. DOI: 10.1016/j.mechmat.2021.103890.
  • A. Alderson, and K. E. Evans, Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure, Phys. Chem. Miner., vol. 28, no. 10, pp. 711–718, 2001.
  • J. Gao, H. Xue, L. Gao, and Z. Luo, Topology optimization for auxetic metamaterials based on isogeometric analysis, Comput. Methods Appl. Mech. Eng., vol. 352, pp. 211–236, 2019. DOI: 10.1016/j.cma.2019.04.021.
  • E. Andreassen, B. S. Lazarov, and O. Sigmund, Design of manufacturable 3D extremal elastic microstructure, Mech. Mater., vol. 69, no. 1, pp. 1–10, 2014. DOI: 10.1016/j.mechmat.2013.09.018.
  • W. Zhang, Z. Ma, and P. Hu, Mechanical properties of a cellular vehicle body structure with negative Poisson’s ratio and enhanced strength, J. Reinf. Plast. Compos., vol. 33, no. 4, pp. 342–349, 2014. DOI: 10.1177/0731684413510752.
  • S. Babaee, J. Shim, J. C. Weaver, E. R. Chen, N. Patel, and K. Bertoldi , 3D soft metamaterials with negative Poisson’s ratio, Adv. Mater. ., vol. 25, no. 36, pp. 5044–5049, 2013. DOI: 10.1002/adma.201301986.
  • X. Ren, J. Shen, P. Tran, T. D. Ngo, and Y. M. Xie, Design and characterisation of a tunable 3D buckling-induced auxetic metamaterial, Mater. Des., vol. 139, pp. 336–342, 2018. DOI: 10.1016/j.matdes.2017.11.025.
  • W. Liu, N. Wang, T. Luo, and Z. Lin, In-plane dynamic crushing of re-entrant auxetic cellular structure, Mater. Des., vol. 100, pp. 84–91, 2016. DOI: 10.1016/j.matdes.2016.03.086.
  • Y. Liu and X. C. Zhang, The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs, Int. J. Impact. Eng., vol. 36, no. 1, pp. 98–109, 2009. DOI: 10.1016/j.ijimpeng.2008.03.001.
  • H. Wan, H. Ohtaki, S. Kotosaka, and G. Hu, A study of negative Poisson’s ratios in auxetic honeycombs based on a large deflection model, Eur. J. Mech. A: Solids., vol. 23, no. 1, pp. 95–106, 2004. DOI: 10.1016/j.euromechsol.2003.10.006.
  • J. X. Qiao and C. Q. Chen, Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs, Int. J. Impact. Eng., vol. 83, pp. 47–58, 2015. DOI: 10.1016/j.ijimpeng.2015.04.005.
  • X. Wang, B. Wang, Z. Wen, and L. Ma, Fabrication and mechanical properties of CFRP composite three-dimensional double-arrow-head auxetic structure, Compos. Sci. Tech., vol. 164, pp. 92–102, 2018. DOI: 10.1016/j.compscitech.2018.05.014.
  • H. Zhang, Y. Luo, and Z. Kang, Bi-material microstructural design of chiral auxetic metamaterials using topology optimization, Compos. Struct., vol. 195, pp. 232–248, 2018. DOI: 10.1016/j.compstruct.2018.04.058.
  • R. Xia, X. Song, L. Sun, W. Wu, C. Li, T. Cheng, and G. Qian, Mechanical properties of 3D isotropic anti-tetrachiral metastructure, Phys. Status Solidi B., vol. 255, no. 4, pp. 1700343, 2018. DOI: 10.1002/pssb.201700343.
  • M. Fu, F. Liu, and L. Hu, A novel category of 3D chiral material with negative Poisson’s ratio, Compos. Sci. Tech., vol. 160, pp. 111–118, 2018. DOI: 10.1016/j.compscitech.2018.03.017.
  • A. Spadoni and M. Ruzzene, Elasto-static micropolar behavior of a chiral auxetic lattice, J. Mech. Phys. Solids, vol. 60, no. 1, pp. 156–171, 2012. DOI: 10.1016/j.jmps.2011.09.012.
  • Y. Y. Jiang and Y. N. Li, 3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation, Adv. Eng. Mater., vol. 19, no. 2, pp. 1600609, 2017. DOI: 10.1002/adem.201600609.
  • J. N. Grima, L. Missi, K. M. Azzopardi, and R. Gatt, Auxetic perforated mechanical metamaterials with randomly oriented cuts, Adv. Mater., vol. 28, no. 2, pp. 385–389, 2016. DOI: 10.1002/adma.201503653.
  • C. W. Smith, J. N. Grima, and K. E. Evans, A novel mechanism for generating auxetic behaviour in reticulated foams: Missing rib foam model, Acta Mater., vol. 48, no. 17, pp. 4349–4356, 2000. [Database] DOI: 10.1016/S1359-6454(00)00269-X.
  • H. Jopek, Finite element analysis of tunable composite tubes reinforced with auxetic structures, Materials, vol. 10, no. 12, pp. 1359, 2017. DOI: 10.3390/ma10121359.
  • X. Li, Q. Wang, Z. Yang, and Z. Lu, Novel auxetic structures with enhanced mechanical properties, Extreme Mech. Lett., vol. 27, pp. 59–65, 2019. DOI: 10.1016/j.eml.2019.01.002.
  • J. N. Grima, V. Zammit, R. Gatt, A. Alderson, and K. E. Evans, Auxetic behavior from rotating semirigid units, Phys. stat. sol. (b), vol. 244, no. 3, pp. 866–882, 2007. DOI: 10.1002/pssb.200572706.
  • B. Nečemer, S. Glodež, N. Novak, and J. Kramberger, Numerical modelling of a chiral auxetic cellular structure under multiaxial loading conditions, Theor. Appl. Fract. Mech., vol. 107, pp. 102514, 2020. DOI: 10.1016/j.tafmec.2020.102514.
  • K. K. Saxena, R. Das, and E. P. Calius, Three decades of auxetics research − materials with negative Poisson's ratio: a review, Adv. Eng. Mater., vol. 18, no. 11, pp. 1847–1870, 2016. DOI: 10.1002/adem.201600053.
  • J. N. Grima and R. Gatt, Perforated sheets exhibiting negative Poisson’s ratios, Adv. Eng. Mater., vol. 12, n. no. 6, pp. 460–464, 2010. DOI: 10.1002/adem.201000005.
  • M. Wagner, T. Chen, and K. Shea, Large shape transforming 4D auxetic structures, 3D Printing and Additive Manufacturing., vol. 4, no. 3, pp. 133–142, 2017. " DOI: 10.1089/3dp.2017.0027.
  • K. Günaydın, Z. Eren, Z. Kazancı, F. Scarpa, A. M. Grande, and H. S. Türkmen, In-plane compression behavior of anti-tetrachiral and re-entrant lattices, Smart Mater. Struct., vol. 28, no. 11, pp. 115028, 2019. DOI: 10.1088/1361-665X/ab47c9.
  • I. N. Sneddon and D. S. Berry, The classical theory of elasticity. In Elasticity and Plasticity/Elastizität Und Plastizität. Springer, Berlin, pp. 1–126, 1958.
  • Z. Li, K. F. Wang, and B. L. Wang, Indentation resistance of brittle auxetic structures: combining discrete representation and continuum model, Eng. Fract. Mech., vol. 252, pp. 107824, 2021. DOI: 10.1016/j.engfracmech.2021.107824.
  • Q. Liu, 2006. Literature review: materials with negative Poisson’s ratios and potential applications to aerospace and defence no. DSTO-GD-0472. Defence Science and Technology Organisation Victoria (Australia) Air Vehicles Div. https://apps.dtic.mil/sti/citations/ADA460791.
  • H. I. Ewards, and R. J. H. Wanhill, Fracture Mechanics, Edward, Arnold, NY, p. 33, 1986.
  • J. B. Choi, and R. S. Lakes, Fracture toughness of Re-entrant foam materials with a negative Poisson’s ratio: Experiment and Analysis, Int. J. Fract., vol. 80, no. 1, pp. 73–83, 1996. DOI: 10.1007/BF00036481.
  • S. Vyavahare, S. Teraiya, and S. Kumar, Auxetic structures fabricated by material extrusion: an experimental investigation of gradient parameters, RPJ., vol. 27, no. 5, pp. 1041–1058, 2021. DOI: 10.1108/RPJ-05-2020-0107.
  • H. Wang, Z. Lu, Z. Yang, and X. Li, A novel re-entrant auxetic honeycomb with enhanced in-plane impact resistance, Compos. Struct., vol. 208, pp. 758–770, 2019. DOI: 10.1016/j.compstruct.2018.10.024.
  • X. Zhao, Q. Gao, L. Wang, Q. Yu, and Z. Ma, Dynamic crushing of double-arrowed auxetic structure under impact loading, Mater. Des., vol. 160, pp. 527–537, 2018. DOI: 10.1016/j.matdes.2018.09.041.
  • L. Hu, M. Z. Zhou, and H. Deng, Dynamic indentation of auxetic and non-auxetic honeycombs under large deformation, Compos. Struct., vol. 207, pp. 323–330, 2019. DOI: 10.1016/j.compstruct.2018.09.066.
  • M. S. Rad, H. Hatami, R. Alipouri, A. F. Nejad, and F. Omidinasab, Determination of energy absorption in different cellular auxetic structures, Mech. Ind., vol. 20, no. 3, pp. 302, 2019.
  • L. Foster, P. Peketi, T. Allen, T. Senior, O. Duncan, and A. Alderson, Application of auxetic foam in sports helmets, Appl. Sci., vol. 8, no. 3, pp. 354, 2018. DOI: 10.3390/app8030354.
  • P. R. Budarapu, S. S. Yb, and R. Natarajan, Design concepts of an aircraft wing: composite and morphing airfoil with auxetic structures, Front. Struct. Civ. Eng., vol. 10, no. 4, pp. 394–408, 2016. DOI: 10.1007/s11709-016-0352-z.
  • W. Lee, Y. Jeong, J. Yoo, H. Huh, S. J. Park, S. H. Park, and J. Yoon, Effect of auxetic structures on crash behavior of cylindrical tube, Compos. Struct., vol. 208, pp. 836–846, 2019. DOI: 10.1016/j.compstruct.2018.10.068.
  • N. Novak, M. Borovinšek, M. Vesenjak, M. Wormser, C. Körner, S. Tanaka, K. Hokamoto, and Z. Ren, Crushing behavior of graded auxetic structures built from inverted tetrapods under impact, Phys. Status Solidi B., vol. 256, no. 1, pp. 1800040, 2019., DOI: 10.1002/pssb.201800040.
  • A. Farokhi Nejad, R. Alipour, M. Shokri Rad, M. Yazid Yahya, S. S. Rahimian Koloor, and M. Petrů, Using finite element approach for crashworthiness assessment of a polymeric auxetic structure subjected to the axial loading, Polymers., vol. 12, no. 6, pp. 1312, 2020. DOI: 10.3390/polym12061312.
  • T. Shepherd, K. Winwood, P. Venkatraman, A. Alderson, and T. Allen, Validation of a finite element modeling process for auxetic structures under impact, Phys. Status Solidi B., vol. 257, no. 10, pp. 1900197, 2020. DOI: 10.1002/pssb.201900197.
  • C. Qi, A. Remennikov, L. Z. Pei, S. Yang, Z. H. Yu, and T. D. Ngo, Impact and close-in blast response of auxetic honeycomb-cored sandwich panels: experimental tests and numerical simulations, Compos. Struct., vol. 180, pp. 161–178, 2017. DOI: 10.1016/j.compstruct.2017.08.020.
  • H. L. Tan, Z. C. He, K. X. Li, E. Li, A. G. Cheng, and B. Xu, In-plane crashworthiness of re-entrant hierarchical honeycombs with negative Poisson’s ratio, Compos. Struct., vol. 229, pp. 111415, 2019. DOI: 10.1016/j.compstruct.2019.111415.
  • T. Wang, Z. Li, L. Wang, Z. Ma, and G. M. Hulbert, Dynamic crushing analysis of a three-dimensional re-entrant auxetic cellular structure, Materials, vol. 12, no. 3, pp. 460, 2019. DOI: 10.3390/ma12030460.
  • H. Jiang, Y. Ren, Q. Jin, G. Zhu, Y. Hu, and F. Cheng, Crashworthiness of novel concentric auxetic reentrant honeycomb with negative Poisson's ratio biologically inspired by coconut palm, Thin-Walled Struct., vol. 154, pp. 106911, 2020. DOI: 10.1016/j.tws.2020.106911.
  • X. C. Zhang, C. C. An, Z. F. Shen, H. X. Wu, W. G. Yang, and J. P. Bai, Dynamic crushing responses of bio-inspired re-entrant auxetic honeycombs under in-plane impact loading, Mater. Today Commun., vol. 23, pp. 100918, 2020. DOI: 10.1016/j.mtcomm.2020.100918.
  • J. Simpson, and Z. Kazancı, Crushing investigation of crash boxes filled with honeycomb and re-entrant (auxetic) lattices, Thin-Walled Struct., vol. 150, pp. 106676, 2020. DOI: 10.1016/j.tws.2020.106676.
  • T. Wang, Z. Li, L. Wang, and G. M. Hulbert, Crashworthiness analysis and collaborative optimization design for a novel crash-box with re-entrant auxetic core, Struct. Multidisc. Optim., vol. 62, no. 4, pp. 2167–2179, 2020. DOI: 10.1007/s00158-020-02568-6.
  • M. S. Rad, Y. Prawoto, and Z. Ahmad, Analytical solution and finite element approach to the 3D re-entrant structures of auxetic materials, Mech. Mater., vol. 74, pp. 76–87, 2014. DOI: 10.1016/j.mechmat.2014.03.012.
  • Q. Gao, C. Ge, W. Zhuang, L. Wang, and Z. Ma, Crashworthiness analysis of double-arrowed auxetic structure under axial impact loading, Mater. Design, vol. 161, pp. 22–34, 2019. DOI: 10.1016/j.matdes.2018.11.013.
  • Q. Gao, X. Zhao, C. Wang, L. Wang, and Z. Ma, Multi-objective crashworthiness optimization for an auxetic cylindrical structure under axial impact loading, Mater. Design, vol. 143, pp. 120–130, 2018. DOI: 10.1016/j.matdes.2018.01.063.
  • Q. Gao, X. Zhao, C. Wang, L. Wang, and Z. Ma, Crashworthiness analysis of a cylindrical auxetic structure under axial impact loading, Sci. China Technol. Sci., vol. 63, no. 1, pp. 140–154, 2020. DOI: 10.1007/s11431-018-9467-6.
  • A. Airoldi, N. Novak, F. Sgobba, A. Gilardelli, and M. Borovinšek, Foam-filled energy absorbers with auxetic behaviour for localized impacts, Mater. Sci. Eng, A, vol. 139500, 2020. DOI: 10.1016/j.msea.2020.139500.
  • M. Najafi, H. Ahmadi, and G. Liaghat, Experimental investigation on energy absorption of auxetic structures, Mater. Today: Proc., v., vol. 34, pp. 350–355, 2021. DOI: 10.1016/j.matpr.2020.06.075.
  • S. Linforth, T. Ngo, P. Tran, D. Ruan, and R. Odish, Investigation of the auxetic oval structure for energy absorption through quasi-static and dynamic experiments, Int. J. Impact Eng., vol. 147, pp. 103741, 2021. DOI: 10.1016/j.ijimpeng.2020.103741.
  • Q. Gao, and W.-H. Liao, Energy absorption of thin walled tube filled with gradient auxetic structures-theory and simulation, Int. J. Mech. Sci. vol. 201, pp. 106475, 2021. DOI: 10.1016/j.ijmecsci.2021.106475.
  • M. Parvaresh, H. Ahmadi, and G. Liaghat, Investigation on the energy absorption of elastomeric auxetic structures in quasi-static and impact loading, J. Sci. Technol. Compos., 2021. DOI: 10.22068/jstc.2021.528762.1719.
  • D. Gao, S. Wang, M. Zhang, and C. Zhang, Experimental and numerical investigation on in-plane impact behaviour of chiral auxetic structure, Compos. Struct. v., vol. 267, pp. 113922, 2021. DOI: 10.1016/j.compstruct.2021.113922.
  • F. Baertsch, A. Ameli, and T. Mayer, Finite-element modeling and optimization of 3D-printed auxetic reentrant structures with stiffness gradient under low-velocity impact, J. Eng. Mech., v., vol. 147, n. no. 7, pp. 04021036, 2021.
  • S. Vyavahare, S. Teraiya, and S. Kumar, An Experimental Study of Influence of Gradient Parameters on Compressive Strength, Stiffness, and Specific Energy Absorption (SEA) of Auxetic Structures Fabricated by FDM. In: Advances in Manufacturing Processes, Springer, Singapore, 2021. p. 305–318
  • H. Sun, Crashworthiness of sandwich cylinder filled with double-arrowed auxetic structures under axial impact loading, Int. J. Crashworthiness., pp. 1–10, 2021. DOI: 10.1080/13588265.2021.1947071
  • H. Tan, Z. He, E. Li, A. Cheng, T. Chen, X. Tan, Q. Li, and B. Xu, Crashworthiness design and multi-objective optimization of a novel auxetic hierarchical honeycomb crash box, Struct. Multidiscip. Optim., pp. 1–16, 2021. DOI: 10.1007/s00158-021-02961-9.
  • F. Steffens, F.R. Oliveira, and R. Fangueiro, Energy absorption from composite reinforced with high performance auxetic textile structure, J. Compos. Mater., v., vol. 55, n. no. 7, pp. 1003–1013, 2021. DOI: 10.1177/0021998320964552.
  • Y. Guo, J. Zhang, L. Chen, B. Du, H. Liu, L. Chen, W. Li, & Y. Liu, Deformation behaviors and energy absorption of auxetic lattice cylindrical structures under axial crushing load, Aerosp. Sci. Technol., vol. 98, pp. 105662, 2020. DOI: 10.1016/j.ast.2019.105662.
  • F. Usta, O. F. Ertaş, A. Ataalp, H. S. Türkmen, Z. Kazancı, and F. Scarpa, Impact behavior of triggered and non-triggered crash tubes with auxetic lattices, Multiscale Multidiscip. Model. Exp. Des., vol. 2, no. 2, pp. 119–127, 2019. DOI: 10.1007/s41939-018-00040-z.
  • W. Hou, X. Yang, W. Zhang, and Y. Xia, Design of energy-dissipating structure with functionally graded auxetic cellular material, Int. J. Crashworthiness, vol. 23, no. 4, pp. 366–376, 2018. DOI: 10.1080/13588265.2017.1328764.
  • H. C. Cheng, F. Scarpa, T. H. Panzera, I. Farrow, and H. X. Peng, Shear stiffness and energy absorption of auxetic open cell foams as sandwich cores, Phys. Status Solidi B, vol. 256, no. 1, pp. 1800411, 2019. DOI: 10.1002/pssb.201800411.
  • T. Fíla, P. Zlámal, O. Jiroušek, J. Falta, P. Koudelka, D. Kytýř, T. Doktor, and J. Valach, Impact Testing of Polymer‐filled Auxetics Using Split Hopkinson Pressure Bar, Adv. Eng. Mater., vol. 19, no. 10, pp. 1700076, 2017.,. DOI: 10.1002/adem.201700076.
  • N. Novak, M. Vesenjak, and Z. Ren, Crush behaviour of auxetic cellular structures, Sci. Technol. Mater., vol. 30, no. 1, pp. 4–7, 2018. DOI: 10.1016/j.stmat.2017.12.003.
  • S. Hou, T. Liu, Z. Zhang, X. Han, and Q. Li, How does negative Poisson’s ratio of foam filler affect crashworthiness?, Mater. Design, vol. 82, pp. 247–259, 2015. DOI: 10.1016/j.matdes.2015.05.050.
  • Z. Li, Q. Gao, S. Yang, L. Wang, and J. Tang, Comparative study of the in-plane uniaxial and biaxial crushing of hexagonal, re-entrant, and mixed honeycombs, J. Sandwich Struct. Mater., vol. 21, no. 6, pp. 1991–2013, 2019. DOI: 10.1177/1099636218755294.
  • H. Al-Rifaie and W. Sumelka, The development of a new shock absorbing uniaxial graded auxetic damper (UGAD), Materials, vol. 12, no. 16, pp. 2573, 2019. DOI: 10.3390/ma12162573.
  • W. L. Azoti, N. Bonfoh, Y. Koutsawa, S. Belouettar, and P. Lipinski, Influence of auxeticity of reinforcements on the overall properties of viscoelastic composite materials, Mech. Mater., vol. 61, pp. 28–38, 2013., DOI: 10.1016/j.mechmat.2013.02.002.
  • R. Chandra, S. P. Singh, and K. Gupta, Damping studies in fiber-reinforced composites–a review, Compos. Struct., vol. 46, no. 1, pp. 41–51, 1999. DOI: 10.1016/S0263-8223(99)00041-0.
  • Y. L. Chen, X. T. Wang, and L. Ma, Damping mechanisms of CFRP three-dimensional double-arrow-head auxetic metamaterials, Polym. Test, vol. 81, pp. 106189, 2020. DOI: 10.1016/j.polymertesting.2019.106189.
  • Y. L. Chen, D. W. Wang, and L. Ma, Vibration and damping performance of carbon fiber-reinforced polymer 3D double-arrow-head auxetic metamaterials, J. Mater. Sci., vol. 56, no. 2, pp. 1443–1460, 2021. DOI: 10.1007/s10853-020-05366-z.
  • Y. Wang, W. Zhao, G. Zhou, Q. Gao, and C. Wang, Optimization of an auxetic jounce bumper based on Gaussian process metamodel and series hybrid GA-SQP algorithm, Struct. Multidisc. Optim., vol. 57, no. 6, pp. 2515–2525, 2018. DOI: 10.1007/s00158-017-1869-z.
  • L. Boldrin, S. Hummel, F. Scarpa, D. Di Maio, C. Lira, M. Ruzzene, C.D.L. Remillat, T.C. Lim, and S. Patsias, Dynamic behaviour of auxetic gradient composite hexagonal honeycombs, Compos. Struct., vol. 149, pp. 114–124, 2016. DOI: 10.1016/j.compstruct.2016.03.044.
  • Y. Ma, F. Scarpa, D. Zhang, B. Zhu, L. Chen, and J. Hong, A nonlinear auxetic structural vibration damper with metal rubber particles, Smart Mater. Struct., vol. 22, no. 8, pp. 084012, 2013. DOI: 10.1088/0964-1726/22/8/084012.
  • K. Essassi, J. L. Rebiere, A.E. Mahi, M.A.B. Souf, A. Bouguecha, and M. Haddar, Experimental and numerical analysis of the dynamic behavior of a bio-based sandwich with an auxetic core, J. Sandwich Struct. Mater., pp. 1099636219851547, 2019. DOI: 10.1177/1099636219851547.
  • X.W. Zhang, and D.Q. Yang, Numerical and experimental studies of a light-weight auxetic cellular vibration isolation base, Shock Vib., vol. 2016, pp. 1–16, 2016. DOI: 10.1155/2016/4017534.
  • N.D. Duc, K. Seung-Eock, N.D. Tuan, P. Tran, and N.D. Khoa, New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer, Aerosp. Sci. Technol., vol. 70, pp. 396–404, 2017. DOI: 10.1016/j.ast.2017.08.023.
  • Q. Li, and D. Yang, Vibro-acoustic performance and design of annular cellular structures with graded auxetic mechanical metamaterials, J. Sound Vib. ., vol. 466, pp. 115038, 2020. DOI: 10.1016/j.jsv.2019.115038.
  • L. Ma, Y. L. Chen, J. S. Yang, X. T. Wang, G. L. Ma, R. Schmidt, and K. U. Schröder, Modal characteristics and damping enhancement of carbon fiber composite auxetic double-arrow corrugated sandwich panels, Compos. Struct., vol. 203, pp. 539–550, 2018. DOI: 10.1016/j.compstruct.2018.07.006.
  • G. J. Murray and F. Gandhi, Auxetic honeycombs with lossy polymeric infills for high damping structural materials, J. Intell. Mater. Syst. Struct., vol. 24, no. 9, pp. 1090–1104, 2013. DOI: 10.1177/1045389X13480569.
  • M. Bianchi and F. Scarpa, Vibration transmissibility and damping behaviour for auxetic and conventional foams under linear and nonlinear regimes, Smart Mater. Struct., vol. 22, no. 8, pp. 084010, 2013. DOI: 10.1088/0964-1726/22/8/084010.
  • B. T. Maruszewski, A. Drzewiecki, and R. Starosta, Thermoelastic damping in an auxetic rectangular plate with thermal relaxation—free vibrations, Smart Mater. Struct., vol. 22, no. 8, pp. 084003, 2013. DOI: 10.1088/0964-1726/22/8/084003.
  • D. D. Nguyen and C. H. Pham, Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson’s ratio in auxetic honeycombs, J. Sandwich Struct. Mater., vol. 20, no. 6, pp. 692–717, 2018. DOI: 10.1177/1099636216674729.
  • M. Ranjbar, L. Boldrin, F. Scarpa, S. Neild, and S. Patsias, Vibroacoustic optimization of anti-tetrachiral and auxetic hexagonal sandwich panels with gradient geometry, Smart Mater. Struct., vol. 25, no. 5, pp. 054012, 2016. DOI: 10.1088/0964-1726/25/5/054012.
  • X. Zhu, J. Zhang, W. Zhang, and J. Chen, Vibration frequencies and energies of an auxetic honeycomb sandwich plate, Mech. Adv. Mater. Struct., vol. 26, no. 23, pp. 1951–1957, 2019. DOI: 10.1080/15376494.2018.1455933.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.