Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Chetna Srivastava; Lalit Bhola; Vinyas Mahesh; P. J. Guruprasad; Nik Petrinic; Fabrizio Scarpa; Dineshkumar Harursampath; Sathiskumar A. Ponnusami

doi:10.1038/s41598-023-47525-7

journal article Open Access Nov 27, 2023

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Chetna Srivastava Lalit Bhola Vinyas Mahesh

P. J. Guruprasad Nik Petrinic Fabrizio Scarpa

Dineshkumar Harursampath Sathiskumar A. Ponnusami

Scientific Reports Vol. 13 No. 1 · Springer Science and Business Media LLC

View at Publisher Save 10.1038/s41598-023-47525-7

Abstract

AbstractClassical approaches to enhance auxeticity quite often involve exploring or designing newer architectures. In this work, simple geometrical features at the member level are engineered to exploit non-classical nonlinearities and improve the auxetic behaviour. The structural elements of the auxetic unit cell are here represented by thin strip-like beams, or thin-walled tubular beams. The resulting nonlinear stiffness enhances the auxeticity of the lattices, especially under large deformations. To quantify the influence of the proposed structural features on the resulting Poisson’s ratio, we use here variational asymptotic method (VAM) and geometrically exact beam theory. The numerical examples reveal that 2D re-entrant type micro-structures made of thin strips exhibit an improvement in terms of auxetic behaviour under compression. For the auxetic unit cell with thin circular tubes as members, Brazier’s effect associated with cross-sectional ovalisation improves the auxetic behaviour under tension; the enhancement is even more significant for the 3D re-entrant geometry. Thin strip-based auxetic unit cells were additively manufactured and tested under compression to verify the numerical observations. The experimentally measured values of the negative Poisson’s ratio are in close agreement with the numerical results, revealing a 66% increase due to the nonlinearity. Simulation results showcase these alternative approaches to improve the auxetic behaviour through simple geometric engineering of the lattice ribs.

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References

55

[1]

Kolken, H. M. A. & Zadpoor, A. A. Auxetic mechanical metamaterials. RSC Adv. 7(9), 5111–5129. https://doi.org/10.1039/C6RA27333E (2017). 10.1039/c6ra27333e

[2]

On the application of additive manufacturing methods for auxetic structures: a review

Athul Joseph, Vinyas Mahesh, Dineshkumar Harursampath

Advances in Manufacturing 2021 10.1007/s40436-021-00357-y

[3]

Smith, C. W., Grima, J. & Evans, K. A novel mechanism for generating auxetic behavior in reticulated foams: missing rib foam model. Acta Mater. 48(17), 4349–4356. https://doi.org/10.1016/S1359-6454(00)00269-X (2000). 10.1016/s1359-6454(00)00269-x

[4]

Koudelka, P., Jirousek, O., Fıla, T. & Doktor, T. Compressive properties of auxetic structures produced with direct 3D printing. Mater. Tehnol. 50(06), 311–317 (2016). https://doi.org/10.17222/mit.2014.204. 10.17222/mit.2014.204

[5]

Liu, W., Li, H., Yang, Z., Zhang, J. & Ge, X. In-plane elastic properties of a 2D chiral cellular structure with V-shaped wings. Eng. Struct. 210, 110384. https://doi.org/10.1016/j.engstruct.2020.110384 (2020). 10.1016/j.engstruct.2020.110384

[6]

Scarpa, F., Panayiotou, P. & Tomlinson, G. Numerical and experimental uniaxial loading on in-plane auxetic honeycombs. J. Strain Anal. Eng. Des. 35(5), 383–388. https://doi.org/10.1243/0309324001514152 (2000). 10.1243/0309324001514152

[7]

Tang, C., Li, L., Wang, L., Herencia, V. Z. & Ren, J. Numerical and experimental studies on the deformation of missing-rib and mixed structures under compression. Phys. Status Solidi (B) 257(10), 2000150. https://doi.org/10.1002/pssb.202000150 (2020). 10.1002/pssb.202000150

[8]

Shokri Rad, M., Ahmad, Z. & Alias, A. Computational approach in formulating mechanical characteristics of 3D star honeycomb auxetic structure. Adv. Mater. Sci. Eng. 2015, 1–11. https://doi.org/10.1155/2015/650769 (2015). 10.1155/2015/650769

[9]

Remennikov, A. et al. Development and performance evaluation of large-scale auxetic protective systems for localized impulsive loads. Int. J. Protect. Struct. 10, 390–417. https://doi.org/10.1177/2041419619858087 (2019). 10.1177/2041419619858087

[10]

Qi, C., Jiang, F., Yu, C. & Yang, S. In-plane crushing response of tetra-chiral honeycombs. Int. J. Impact Eng 130, 247–265. https://doi.org/10.1016/j.ijimpeng.2019.04.019 (2019). 10.1016/j.ijimpeng.2019.04.019

[11]

Li, C., Shen, H.-S. & Wang, H. Full-scale finite element modeling and nonlinear bending analysis of sandwich plates with functionally graded auxetic 3D lattice core. J. Sandwich Struct. Mater. 23(7), 13–3138. https://doi.org/10.1177/1099636220924657 (2021). 10.1177/1099636220924657

[12]

Dutta, S., Menon, H. G., Hariprasad, M., Krishnan, A. & Shankar, B. Study of auxetic beams under bending: A finite element approach. Mater. Today Proc. 46, 9782–9787. https://doi.org/10.1016/j.matpr.2020.10.479 (2021). 10.1016/j.matpr.2020.10.479

[13]

Li, T., Chen, Y., Hu, X., Li, Y. & Wang, L. Exploiting negative Poisson’s ratio to design 3D-printed composites with enhanced mechanical properties. Mater. Des. 142, 247–258. https://doi.org/10.1016/j.matdes.2018.01.034 (2018). 10.1016/j.matdes.2018.01.034

[14]

Fozdar, D. Y., Soman, P., Lee, J. W., Han, L.-H. & Chen, S. Three-dimensional polymer constructs exhibiting a tunable negative Poisson’s ratio. Adv. Funct. Mater. 21, 2712–2720. https://doi.org/10.1002/adfm.201002022 (2011). 10.1002/adfm.201002022

[15]

A novel hybrid-honeycomb structure: Enhanced stiffness, tunable auxeticity and negative thermal expansion

Xiang-Long Peng, Swantje Bargmann

International Journal of Mechanical Sciences 2021 10.1016/j.ijmecsci.2020.106021

[16]

Wei, L., Zhao, X., Yu, Q. & Zhu, G. A novel star auxetic honeycomb with enhanced in-plane crushing strength. Thin-Wall. Struct. 149, 106623. https://doi.org/10.1016/j.tws.2020.106623 (2020). 10.1016/j.tws.2020.106623

[17]

Elipe, J. C. A. & Lantada, A. D. Comparative study of auxetic geometries by means of computer-aided design and engineering. Smart Mater. Struct. 21(10), 105004. https://doi.org/10.1088/0964-1726/21/10/105004 (2012). 10.1088/0964-1726/21/10/105004

[18]

Grima, J. N., Gatt, R., Alderson, A. & Evans, K. On the potential of connected stars as auxetic systems. Mol. Simul. 31(13), 925–935. https://doi.org/10.1080/08927020500401139 (2005). 10.1080/08927020500401139

[19]

Jiang, W. et al. Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review. Compos. B Eng. 235, 109733. https://doi.org/10.1016/j.compositesb.2022.1097334 (2022). 10.1016/j.compositesb.2022.1097334

[20]

Gatt, R. et al. Hierarchical auxetic mechanical metamaterials. Sci. Rep. 5, 8395. https://doi.org/10.1038/srep08395 (2015). 10.1038/srep08395

[21]

Eghbali, P. et al. Study in circular auxetic structures for efficiency enhancement in piezoelectric vibration energy harvesting. Sci. Rep. 10, 16338. https://doi.org/10.1038/s41598-020-73425-1 (2020). 10.1038/s41598-020-73425-1

[22]

Wang, H. et al. Modulation of multi-directional auxeticity in hybrid origami metamaterials. Appl. Mat. Today 20, 100715. https://doi.org/10.1016/j.apmt.2020.100715 (2020). 10.1016/j.apmt.2020.100715

[23]

Sigmund, O. Topology optimization: A tool for the tailoring of structures and materials. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 358, 211–227. https://doi.org/10.1098/rsta.2000.0528 (2000). 10.1098/rsta.2000.0528

[24]

Fu, M., Liu, F. & Hu, L. A novel category of 3D chiral material with negative Poisson’s ratio. Compos. Sci. Technol. 160, 111–118. https://doi.org/10.1016/j.compscitech.2018.03.017 (2018). 10.1016/j.compscitech.2018.03.017

[25]

Javadi, A., Faramarzi, A. & Farmani, R. Design and optimization of microstructure of auxetic materials. Eng. Comput. 29, 260–276. https://doi.org/10.1108/02644401211212398 (2012). 10.1108/02644401211212398

[26]

Wang, Z.-P., Poh, L. H., Zhu, Y., Dirrenberger, J. & Forest, S. Systematic design of tetra-petals auxetic structures with stiffness constraint. Mater. Des. 170, 107669. https://doi.org/10.1016/j.matdes.2019.107669 (2019). 10.1016/j.matdes.2019.107669

[27]

Harkati, A. et al. In-plane elastic constants of a new curved cell walls honeycomb concept. Thin-Wall. Struct. 149, 106613. https://doi.org/10.1016/j.tws.2020.106613 (2020). 10.1016/j.tws.2020.106613

[28]

Zhang, W., Zhao, S., Sun, R., Scarpa, F. & Wang, J. In-plane mechanical behavior of a new star-re-entrant hierarchical metamaterial. Polymers https://doi.org/10.3390/polym11071132 (2021). 10.3390/polym11071132

[29]

Zhang, Q. et al. Large stiffness thermoformed open cell foams with auxeticity. Appl. Mater. Today 20, 100775. https://doi.org/10.1016/j.apmt.2020.100775 (2020). 10.1016/j.apmt.2020.100775

[30]

Bianchi, M., Scarpa, F. & Smith, C. Shape memory behaviour in auxetic foams: Mechanical properties. Acta Mater. 58(3), 858–865. https://doi.org/10.1016/j.actamat.2009.09.063 (2010). 10.1016/j.actamat.2009.09.063

[31]

Gatt, R. et al. A realistic generic model for anti-tetrachiral systems. Phys. Status Solidi (B) https://doi.org/10.1002/pssb.201384246 (2013). 10.1002/pssb.201384246

[32]

Mousanezhad, D. et al. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach. Theor. Appl. Mech. Lett. 6(2), 81–96. https://doi.org/10.1016/j.taml.2016.02.004 (2016). 10.1016/j.taml.2016.02.004

[33]

Tabacu, S., Negrea, R. F. & Negrea, D. Experimental, numerical and analytical investigation of 2D tetra-anti-chiral structure under compressive loads. Thin-Wall. Struct. 155, 106929. https://doi.org/10.1016/j.tws.2020.106929 (2020). 10.1016/j.tws.2020.106929

[34]

Mukhopadhyay, T. & Adhikari, S. Effective in-plane elastic properties of auxetic honeycombs with spatial irregularity. Mechanics of Materials 95, 204–222. https://doi.org/10.1016/j.mechmat.2016.01.009 (2016). 10.1016/j.mechmat.2016.01.009

[35]

Wang, T., Wang, L., Ma, Z. & Hulbert, G. M. Elastic analysis of auxetic cellular structure consisting of re-entrant hexagonal cells using a strain-based expansion homogenization method. Mater. Des. 160, 284–293. https://doi.org/10.1016/j.matdes.2018.09.013 (2018). 10.1016/j.matdes.2018.09.013

[36]

Theocaris, P., Stavroulakis, G. & Panagiotopoulos, P. Negative Poisson’s ratios in composites with star-shaped inclusions: A numerical homogenization approach. Arch. Appl. Mech. 67(4), 274–286. https://doi.org/10.1007/s004190050117 (1997). 10.1007/s004190050117

[37]

Srivastava, C. et al. Effective Mechanical Properties of Auxetic Materials: Numerical Predictions Using Variational Asymptotic Method Based Homogenization Abstract. J. Appl. Mechan 90(11). https://doi.org/10.1115/1.4062845 (2023). 10.1115/1.4062845

[38]

Nika, G. & Constantinescu, A. Design of multi-layer materials using inverse homogenization and a level set method. Comput. Methods Appl. Mech. Eng. 346, 388–409. https://doi.org/10.1016/j.cma.2018.11.029 (2019). 10.1016/j.cma.2018.11.029

[39]

Sigmund, O. Materials with prescribed constitutive parameters: An inverse homogenization problem. Int. J. Solids Struct. 31(17), 2313–2329. https://doi.org/10.1016/0020-7683(94)90154-6 (1994). 10.1016/0020-7683(94)90154-6

[40]

Wan, H., Ohtaki, H., Kotosaka, S. & Hu, G. A study of negative Poisson’s ratios in auxetic honeycombs based on a large deflection model. Eur. J. Mech. A/Solids 23(1), 95–106. https://doi.org/10.1016/j.euromechsol.2003.10.006 (2004). 10.1016/j.euromechsol.2003.10.006

[41]

Levy, O., Krylov, S. & Goldfarb, I. Design considerations for negative Poisson ratio structures under large deflection for MEMS applications. Smart Mater. Struct. 15, 1459–1466. https://doi.org/10.1088/0964-1726/15/5/035 (2006). 10.1088/0964-1726/15/5/035

[42]

Gao, Q. et al. Theoretical, numerical and experimental analysis of three-dimensional double-v honeycomb. Mater. Des. 139, 380–391. https://doi.org/10.1016/j.matdes.2017.11.024 (2018). 10.1016/j.matdes.2017.11.024

[43]

Zhang, J., Lu, G. & You, Z. Large deformation and energy absorption of additively manufactured auxetic materials and structures: A review. Compos. Part B Eng. 201, 108340. https://doi.org/10.1016/j.compositesb.2020.108340 (2020). 10.1016/j.compositesb.2020.108340

[44]

Hu, L., Luo, Z., Zhang, Z., Lian, M. & Huang, L. Mechanical property of re-entrant anti-trichiral honeycombs under large deformation. Compos. Part B Eng. 163, 107–120. https://doi.org/10.1016/j.compositesb.2018.11.010 (2019). 10.1016/j.compositesb.2018.11.010

[45]

Jiang, Y., Rudra, B., Shim, J. & Li, Y. Limiting strain for auxeticity under large compressive deformation: Chiral vs. re-entrant cellular solids. Int. J. Solids Struct. 162, 87–95. https://doi.org/10.1016/j.ijsolstr.2018.11.035 (2019). 10.1016/j.ijsolstr.2018.11.035

[46]

Hodges, D. H., Harursampath, D., Volovoi, V. V. & Cesnik, C. E. Non-classical effects in non-linear analysis of pretwisted anisotropic strips. Int. J. Non-Linear Mech. 34(2), 259–277. https://doi.org/10.1016/S0020-7462(98)00023-7 (1999). 10.1016/s0020-7462(98)00023-7

[47]

Harursampath, D. & Hodges, D. H. Asymptotic analysis of the non-linear behavior of long anisotropic tubes. Int. J. Non-linear Mech. 34(6), 1003–1018. https://doi.org/10.1016/S0020-7462(98)00070-5 (1999). 10.1016/s0020-7462(98)00070-5

[48]

Ponnusami, S. A., Gupta, M. & Harursampath, D. Asymptotic modeling of nonlinear bending and buckling behavior of carbon nanotubes. AIAA J. 57(10), 4132–4140. https://doi.org/10.2514/1.J057564 (2019). 10.2514/1.j057564

[49]

Yang, L., Harrysson, O., West, H. & Cormier, D. Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. Int. J. Solids Struct. 69–70, 475–490. https://doi.org/10.1016/j.ijsolstr.2015.05.005 (2015). 10.1016/j.ijsolstr.2015.05.005

[50]

Hodges, D. Nonlinear Compos. Beam Theory https://doi.org/10.2514/4.866821 (2006). 10.2514/4.866821

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Published: Nov 27, 2023
Vol/Issue: 13(1)
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Authors

Bristol Composites Institute (ACCIS), University of Bristol, BS8 1TR Bristol, U.K.

D

Dineshkumar Harursampath

S

Sathiskumar A. Ponnusami

Cite This Article

Chetna Srivastava, Lalit Bhola, Vinyas Mahesh, et al. (2023). Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials. Scientific Reports, 13(1). https://doi.org/10.1038/s41598-023-47525-7

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

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