Exploiting negative Poisson's ratio to design 3D-printed composites with enhanced mechanical properties

Li, Tiantian; Chen, Yanyu; Hu, Xiaoyi; Li, Yangbo; Wang, Lifeng

doi:10.1016/j.matdes.2018.01.034

Title: Exploiting negative Poisson's ratio to design 3D-printed composites with enhanced mechanical properties

Journal Article · Sat Feb 03 00:00:00 EST 2018 · Materials & Design

DOI:https://doi.org/10.1016/j.matdes.2018.01.034· OSTI ID:1424903

Li, Tiantian ^[1]; Chen, Yanyu ^[2]; Hu, Xiaoyi ^[1]; Li, Yangbo ^[3]; Wang, Lifeng ^[1]

Stony Brook Univ., NY (United States)
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Stony Brook Univ., NY (United States); China Three Gorges Univ., Hubei (China)

Auxetic materials exhibiting a negative Poisson's ratio are shown to have better indentation resistance, impact shielding capability, and enhanced toughness. Here, we report a class of high-performance composites in which auxetic lattice structures are used as the reinforcements and the nearly incompressible soft material is employed as the matrix. This coupled geometry and material design concept is enabled by the state-of-the-art additive manufacturing technique. Guided by experimental tests and finite element analyses, we systematically study the compressive behavior of the 3D printed auxetics reinforced composites and achieve a significant enhancement of their stiffness and energy absorption. This improved mechanical performance is due to the negative Poisson's ratio effect of the auxetic reinforcements, which makes the matrix in a state of biaxial compression and hence provides additional support. This mechanism is further supported by the investigation of the effect of auxetic degree on the stiffness and energy absorption capability. The findings reported here pave the way for developing a new class of auxetic composites that significantly expand their design space and possible applications through a combination of rational design and 3D printing.

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Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: AC36-08GO28308

OSTI ID:: 1424903

Report Number(s):: NREL/JA-5400-71053; TRN: US1801961

Journal Information:: Materials & Design, Vol. 142, Issue C; ISSN 0264-1275

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 203 works

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References (76)

Auxetic polymers: a new range of materials Evans, Ken E. Endeavour, Vol. 15, Issue 4 https://doi.org/10.1016/0160-9327(91)90123-S	journal	January 1991
Negative Poisson's ratios as a common feature of cubic metals Baughman, Ray H.; Shacklette, Justin M.; Zakhidov, Anvar A. Nature, Vol. 392, Issue 6674 https://doi.org/10.1038/32842	journal	March 1998
Do Zeolites Have Negative Poisson’s Ratios? Grima, J. N.; Jackson, R.; Alderson, A. Advanced Materials, Vol. 12, Issue 24 https://doi.org/10.1002/1521-4095(200012)12:24<1912::AID-ADMA1912>3.0.CO;2-7	journal	December 2000
Natrolite: A zeolite with negative Poisson’s ratios Grima, Joseph N.; Gatt, Ruben; Zammit, Victor Journal of Applied Physics, Vol. 101, Issue 8 https://doi.org/10.1063/1.2718879	journal	April 2007
Effect of a Negative Poisson Ratio in the Tension of Ceramics Song, Fan; Zhou, Junbing; Xu, Xianghong Physical Review Letters, Vol. 100, Issue 24 https://doi.org/10.1103/PhysRevLett.100.245502	journal	June 2008
Elasticity of agr-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio Yeganeh-Haeri, A.; Weidner, D. J.; Parise, J. B. Science, Vol. 257, Issue 5070 https://doi.org/10.1126/science.257.5070.650	journal	July 1992
Negative Poisson’s Ratio in Single-Layer Graphene Ribbons Jiang, Jin-Wu; Park, Harold S. Nano Letters, Vol. 16, Issue 4 https://doi.org/10.1021/acs.nanolett.6b00311	journal	March 2016
Tailoring Graphene to Achieve Negative Poisson's Ratio Properties Grima, Joseph N.; Winczewski, Szymon; Mizzi, Luke Advanced Materials, Vol. 27, Issue 8 https://doi.org/10.1002/adma.201404106	journal	December 2014
Self-assembly of coherently dynamic, auxetic, two-dimensional protein crystals Suzuki, Yuta; Cardone, Giovanni; Restrepo, David Nature, Vol. 533, Issue 7603 https://doi.org/10.1038/nature17633	journal	May 2016
Foam Structures with a Negative Poisson's Ratio Lakes, R. Science, Vol. 235, Issue 4792 https://doi.org/10.1126/science.235.4792.1038	journal	February 1987
Indentability of Conventional and Negative Poisson's Ratio Foams Lakes, R. S.; Elms, K. Journal of Composite Materials, Vol. 27, Issue 12 https://doi.org/10.1177/002199839302701203	journal	December 1993
Review on auxetic materials Yang, Wei; Li, Zhong-Ming; Shi, Wei Journal of Materials Science, Vol. 39, Issue 10 https://doi.org/10.1023/B:JMSC.0000026928.93231.e0	journal	May 2004
Auxetic behavior from rotating squares Grima, J. N.; Evans, K. E. Journal of Materials Science Letters, Vol. 19, Issue 17, p. 1563-1565 https://doi.org/10.1023/A:1006781224002	journal	January 2000
Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis Choi, J. B.; Lakes, R. S. International Journal of Fracture, Vol. 80, Issue 1 https://doi.org/10.1007/BF00036481	journal	January 1996
Auxetic materials Alderson, A.; Alderson, K. L. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 221, Issue 4 https://doi.org/10.1243/09544100JAERO185	journal	April 2007
Crashworthiness assessment of auxetic foam-filled tube under quasi-static axial loading Mohsenizadeh, S.; Alipour, R.; Shokri Rad, M. Materials & Design, Vol. 88 https://doi.org/10.1016/j.matdes.2015.08.152	journal	December 2015
How does negative Poisson’s ratio of foam filler affect crashworthiness? Hou, Shujuan; Liu, Taiqu; Zhang, Zhidan Materials & Design, Vol. 82 https://doi.org/10.1016/j.matdes.2015.05.050	journal	October 2015
Bending behavior of sandwich composite structures with tunable 3D-printed core materials Li, Tiantian; Wang, Lifeng Composite Structures, Vol. 175 https://doi.org/10.1016/j.compstruct.2017.05.001	journal	September 2017
Bioinspired Structural Material Exhibiting Post-Yield Lateral Expansion and Volumetric Energy Dissipation During Tension Wang, Lifeng; Boyce, Mary C. Advanced Functional Materials, Vol. 20, Issue 18 https://doi.org/10.1002/adfm.201000282	journal	September 2010
Auxetic materials and their potential applications in textiles Wang, Zhengyue; Hu, Hong Textile Research Journal, Vol. 84, Issue 15 https://doi.org/10.1177/0040517512449051	journal	March 2014
Innovative three-dimensional fabric structure with negative Poisson's ratio for composite reinforcement Ge, Zhaoyang; Hu, Hong Textile Research Journal, Vol. 83, Issue 5 https://doi.org/10.1177/0040517512454185	journal	November 2012
Development of auxetic fabrics using flat knitting technology Textile Research Journal, Vol. 81, Issue 14 https://doi.org/10.1177/0040517511404594	journal	May 2011
Auxetic behaviour: appearance and engineering applications Stavroulakis, G. E. physica status solidi (b), Vol. 242, Issue 3 https://doi.org/10.1002/pssb.200460388	journal	March 2005
Auxetic materials for bioprostheses [In the Spotlight] Scarpa, Fabrizio IEEE Signal Processing Magazine, Vol. 25, Issue 5 https://doi.org/10.1109/MSP.2008.926663	journal	September 2008
Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers Wojciechowski, K. W. Molecular Physics, Vol. 61, Issue 5 https://doi.org/10.1080/00268978700101761	journal	August 1987
Computer simulations of auxetic foams in two dimensions Pozniak, A. A.; Smardzewski, J.; Wojciechowski, K. W. Smart Materials and Structures, Vol. 22, Issue 8 https://doi.org/10.1088/0964-1726/22/8/084009	journal	July 2013
Computation of the homogenized nonlinear elastic response of 2D and 3D auxetic structures based on micropolar continuum models El Nady, K.; Dos Reis, F.; Ganghoffer, J. F. Composite Structures, Vol. 170 https://doi.org/10.1016/j.compstruct.2017.02.043	journal	June 2017
Properties of a chiral honeycomb with a poisson's ratio of — 1 Prall, D.; Lakes, R. S. International Journal of Mechanical Sciences, Vol. 39, Issue 3 https://doi.org/10.1016/S0020-7403(96)00025-2	journal	March 1997
A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model Smith, C. W.; Grima, J. N.; Evans, K. E. Acta Materialia, Vol. 48, Issue 17 https://doi.org/10.1016/S1359-6454(00)00269-X	journal	November 2000
3D Printed Chiral Cellular Solids with Amplified Auxetic Effects Due to Elevated Internal Rotation : 3D Printed Chiral Cellular Solids with Amplified… Jiang, Yunyao; Li, Yaning Advanced Engineering Materials, Vol. 19, Issue 2 https://doi.org/10.1002/adem.201600609	journal	October 2016
Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method Vogiatzis, Panagiotis; Chen, Shikui; Wang, Xiao Computer-Aided Design, Vol. 83 https://doi.org/10.1016/j.cad.2016.09.009	journal	February 2017
Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François Computational Mechanics, Vol. 58, Issue 6 https://doi.org/10.1007/s00466-016-1326-7	journal	September 2016
Designing two-dimensional metamaterials of controlled static and dynamic properties Karathanasopoulos, Nikolaos; Reda, Hilal; Ganghoffer, Jean-francois Computational Materials Science, Vol. 138 https://doi.org/10.1016/j.commatsci.2017.06.035	journal	October 2017
Two-dimensional isotropic system with a negative poisson ratio Wojciechowski, K. W. Physics Letters A, Vol. 137, Issue 1-2 https://doi.org/10.1016/0375-9601(89)90971-7	journal	May 1989
Poisson's ratio of rectangular anti-chiral structures with size dispersion of circular nodes: Poisson's ratio of rectangular anti-chiral structures Pozniak, A. A.; Wojciechowski, K. W. physica status solidi (b), Vol. 251, Issue 2 https://doi.org/10.1002/pssb.201384256	journal	January 2014
Auxetic behaviour from rotating rigid units Grima, J. N.; Alderson, A.; Evans, K. E. physica status solidi (b), Vol. 242, Issue 3 https://doi.org/10.1002/pssb.200460376	journal	March 2005
Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots Milton, Graeme Walter Journal of the Mechanics and Physics of Solids, Vol. 61, Issue 7 https://doi.org/10.1016/j.jmps.2012.08.011	journal	July 2013
Reentrant Origami-Based Metamaterials with Negative Poisson’s Ratio and Bistability Yasuda, H.; Yang, J. Physical Review Letters, Vol. 114, Issue 18 https://doi.org/10.1103/PhysRevLett.114.185502	journal	May 2015
Graded conventional-auxetic Kirigami sandwich structures: Flatwise compression and edgewise loading Hou, Y.; Neville, R.; Scarpa, F. Composites Part B: Engineering, Vol. 59 https://doi.org/10.1016/j.compositesb.2013.10.084	journal	March 2014
Design of planar isotropic negative Poisson’s ratio structures Shan, Sicong; Kang, Sung H.; Zhao, Zhenhao Extreme Mechanics Letters, Vol. 4 https://doi.org/10.1016/j.eml.2015.05.002	journal	September 2015
Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility Tang, Yichao; Yin, Jie Extreme Mechanics Letters, Vol. 12 https://doi.org/10.1016/j.eml.2016.07.005	journal	April 2017
Directing the Deformation Paths of Soft Metamaterials with Prescribed Asymmetric Units Wu, Gaoxiang; Cho, Yigil; Choi, In-Suk Advanced Materials, Vol. 27, Issue 17 https://doi.org/10.1002/adma.201500716	journal	March 2015
Engineering the shape and structure of materials by fractal cut Cho, Yigil; Shin, Joong-Ho; Costa, Avelino Proceedings of the National Academy of Sciences, Vol. 111, Issue 49 https://doi.org/10.1073/pnas.1417276111	journal	November 2014
Design of Hierarchically Cut Hinges for Highly Stretchable and Reconfigurable Metamaterials with Enhanced Strength Tang, Yichao; Lin, Gaojian; Han, Lin Advanced Materials, Vol. 27, Issue 44 https://doi.org/10.1002/adma.201502559	journal	October 2015
Negative Poisson coefficient of fractal structures Novikov, V. V.; Wojciechowski, K. W. Physics of the Solid State, Vol. 41, Issue 12 https://doi.org/10.1134/1.1131137	journal	December 1999
Auxeticity of Yukawa Systems with Nanolayers in the (111) Crystallographic Plane Pigłowski, Paweł; Narojczyk, Jakub; Poźniak, Artur Materials, Vol. 10, Issue 11 https://doi.org/10.3390/ma10111338	journal	November 2017
Single fibre pullout tests on auxetic polymeric fibres Simkins, V. R.; Alderson, A.; Davies, P. J. Journal of Materials Science, Vol. 40, Issue 16 https://doi.org/10.1007/s10853-005-2829-3	journal	August 2005
How to make auxetic fibre reinforced composites Alderson, K. L.; Simkins, V. R.; Coenen, V. L. physica status solidi (b), Vol. 242, Issue 3 https://doi.org/10.1002/pssb.200460371	journal	March 2005
Auxetic fibre networks and their composites Jayanty, Sharmila; Crowe, Jason; Berhan, Lesley physica status solidi (b), Vol. 248, Issue 1 https://doi.org/10.1002/pssb.201083973	journal	August 2010
A finite element analysis of a 3D auxetic textile structure for composite reinforcement Ge, Zhaoyang; Hu, Hong; Liu, Yanping Smart Materials and Structures, Vol. 22, Issue 8 https://doi.org/10.1088/0964-1726/22/8/084005	journal	July 2013
Auxetic composites made of 3D textile structure and polyurethane foam: Auxetic composites made of 3D textile structure and polyurethane foam Zhou, Lin; Jiang, Lili; Hu, Hong physica status solidi (b), Vol. 253, Issue 7 https://doi.org/10.1002/pssb.201552768	journal	March 2016
Planar auxeticity from elliptic inclusions Poźniak, Artur A.; Wojciechowski, Krzysztof W.; Grima, Joseph N. Composites Part B: Engineering, Vol. 94 https://doi.org/10.1016/j.compositesb.2016.03.003	journal	June 2016
Architected Cellular Materials Schaedler, Tobias A.; Carter, William B. Annual Review of Materials Research, Vol. 46, Issue 1 https://doi.org/10.1146/annurev-matsci-070115-031624	journal	July 2016
3D printing of polymer matrix composites: A review and prospective Wang, Xin; Jiang, Man; Zhou, Zuowan Composites Part B: Engineering, Vol. 110 https://doi.org/10.1016/j.compositesb.2016.11.034	journal	February 2017
Impact Testing of Polymer-filled Auxetics Using Split Hopkinson Pressure Bar : Impact Testing of Polymer-filled Auxetics… Fíla, Tomáš; Zlámal, Petr; Jiroušek, Ondřej Advanced Engineering Materials, Vol. 19, Issue 10 https://doi.org/10.1002/adem.201700076	journal	May 2017
A Preliminary Study of Negative Poisson's Ratio of Laminated Fiber Reinforced Composites Zhang, Ruguang; Yeh, Hsien-Liang; Yeh, Hsien-Yang Journal of Reinforced Plastics and Composites, Vol. 17, Issue 18 https://doi.org/10.1177/073168449801701806	journal	December 1998
Transversely isotropic hyperelastic-viscoplastic model for glassy polymers with application to additive manufactured photopolymers Zhang, Pu; To, Albert C. International Journal of Plasticity, Vol. 80 https://doi.org/10.1016/j.ijplas.2015.12.012	journal	May 2016
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials Arruda, Ellen M.; Boyce, Mary C. Journal of the Mechanics and Physics of Solids, Vol. 41, Issue 2 https://doi.org/10.1016/0022-5096(93)90013-6	journal	February 1993
Models for the elastic deformation of honeycombs Masters, I. G.; Evans, K. E. Composite Structures, Vol. 35, Issue 4 https://doi.org/10.1016/S0263-8223(96)00054-2	journal	August 1996
Auxetic mechanical metamaterials Kolken, H. M. A.; Zadpoor, A. A. RSC Advances, Vol. 7, Issue 9 https://doi.org/10.1039/C6RA27333E	journal	January 2017
3D Soft Metamaterials with Negative Poisson's Ratio Babaee, Sahab; Shim, Jongmin; Weaver, James C. Advanced Materials, Vol. 25, Issue 36 https://doi.org/10.1002/adma.201301986	journal	July 2013
Chiral three-dimensional lattices with tunable Poisson’s ratio Ha, Chan Soo; Plesha, Michael E.; Lakes, Roderic S. Smart Materials and Structures, Vol. 25, Issue 5 https://doi.org/10.1088/0964-1726/25/5/054005	journal	April 2016
Orthotropic Laminated Open-cell Frameworks Retaining Strong Auxeticity under Large Uniaxial Loading Tanaka, Hiro; Suga, Kaito; Iwata, Naoki Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/srep39816	journal	January 2017
Lattice Metamaterials with Mechanically Tunable Poisson’s Ratio for Vibration Control Chen, Yanyu; Li, Tiantian; Scarpa, Fabrizio Physical Review Applied, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevApplied.7.024012	journal	February 2017
Fabrication and characterisation of a fully auxetic 3D lattice structure via selective electron beam melting Warmuth, Franziska; Osmanlic, Fuad; Adler, Lucas Smart Materials and Structures, Vol. 26, Issue 2 https://doi.org/10.1088/1361-665X/26/2/025013	journal	December 2016
Harnessing out-of-plane deformation to design 3D architected lattice metamaterials with tunable Poisson’s ratio Li, Tiantian; Hu, Xiaoyi; Chen, Yanyu Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-09218-w	journal	August 2017
Co-Continuous Composite Materials for Stiffness, Strength, and Energy Dissipation Wang, Lifeng; Lau, Jacky; Thomas, Edwin L. Advanced Materials, Vol. 23, Issue 13 https://doi.org/10.1002/adma.201003956	journal	February 2011
Enhanced Energy Dissipation in Periodic Epoxy Nanoframes Lee, Jae-Hwang; Wang, Lifeng; Kooi, Steven Nano Letters, Vol. 10, Issue 7 https://doi.org/10.1021/nl1012773	journal	May 2010
Enhanced stiffness, strength and energy absorption for co-continuous composites with liquid filler Liu, Yilun; Wang, Lifeng Composite Structures, Vol. 128 https://doi.org/10.1016/j.compstruct.2015.03.064	journal	September 2015
Overview of Current Additive Manufacturing Technologies and Selected Applications Horn, Timothy J.; Harrysson, Ola L. A. Science Progress, Vol. 95, Issue 3 https://doi.org/10.3184/003685012X13420984463047	journal	September 2012
Properties of Ti–6Al–4V non-stochastic lattice structures fabricated via electron beam melting Cansizoglu, O.; Harrysson, O.; Cormier, D. Materials Science and Engineering: A, Vol. 492, Issue 1-2 https://doi.org/10.1016/j.msea.2008.04.002	journal	September 2008
Additive Manufacturing of Ceramics: Issues, Potentialities, and Opportunities Zocca, Andrea; Colombo, Paolo; Gomes, Cynthia M. Journal of the American Ceramic Society, Vol. 98, Issue 7 https://doi.org/10.1111/jace.13700	journal	July 2015
Carbon periodic cellular architectures Szczurek, A.; Ortona, A.; Ferrari, L. Carbon, Vol. 88 https://doi.org/10.1016/j.carbon.2015.02.069	journal	July 2015
Periodic Bicontinuous Composites for High Specific Energy Absorption Lee, Jae-Hwang; Wang, Lifeng; Boyce, Mary C. Nano Letters, Vol. 12, Issue 8 https://doi.org/10.1021/nl302234f	journal	July 2012
Additive manufacturing of polymer-derived ceramics Eckel, Z. C.; Zhou, C.; Martin, J. H. Science, Vol. 351, Issue 6268 https://doi.org/10.1126/science.aad2688	journal	December 2015
Hierarchically Enhanced Impact Resistance of Bioinspired Composites Gu, Grace X.; Takaffoli, Mahdi; Buehler, Markus J. Advanced Materials, Vol. 29, Issue 28 https://doi.org/10.1002/adma.201700060	journal	May 2017

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