Abstract
Mechanical metamaterials are systems which derive their mechanical properties from their structure rather than their intrinsic material composition. In this work, we investigate a class of highly anisotropic mechanical metamaterials designed by the introduction of diamond and elliptically shaped perforations which possess the ability to show auxetic behaviour. By the use of finite element simulations, we show how these highly tuneable systems have the potential to exhibit a large range of Poisson’s ratios, ranging from highly positive to giant negative values, simply by altering the geometric parameters and orientation of the perforations. The anomalous properties of these systems have also been shown to be retained over significant tensile strain ranges, highlighting the vast potential applicability and functionality of these mechanical metamaterials.
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References
Evans, K.E., Nkansah, M.A., Hutchinson, I.J., Rogers, J.A.: Molecular network design. Nature 353, 124 (1991)
Ali, M.N., Rehman, I.U.: Auxetic polyurethane stents and stent-grafts for the palliative treatment of squamous cell carcinomas of the proximal and mid oesophagus: a novel fabrication route. J. Manuf. Syst. (2014). https://doi.org/10.1016/j.jmsy.2014.07.009
Mizzi, L., Attard, D., Casha, A., Grima, J.N., Gatt, R.: On the suitability of hexagonal honeycombs as stent geometries. Phys. Status Solidi B 251, 328–337 (2014). https://doi.org/10.1002/pssb.201384255
Wu, W., Song, X., Liang, J., Xia, R., Qian, G., Fang, D.: Mechanical properties of anti-tetrachiral auxetic stents. Compos. Struct. 185, 381–392 (2018). https://doi.org/10.1016/j.compstruct.2017.11.048
Grima, J.N., Evans, K.E.: Auxetic slit-perforated sheets with a “Rotating Squares” geometry and their applicability for the manufacture of knee and elbow bandages (Personal Communication) (2000)
Wright, J.R., Burns, M.K., James, E., Sloan, M.R., Evans, K.E.: On the design and characterisation of low-stiffness auxetic yarns and fabrics. Text. Res. J. 82, 645–654 (2012)
Wang, Z., Hong, H.: A finite element analysis of an auxetic wrap-knitted spacer fabric structure. Text. Res. J. 85, 404–415 (2014)
Gatt, R., Mizzi, L., Azzopardi, J.I., Azzopardi, K.M., Attard, D., Casha, A., et al.: Hierarchical auxetic mechanical metamaterials. Sci. Rep. 5, 1–6 (2015). https://doi.org/10.1038/srep08395
Mizzi, L., Azzopardi, K.M., Attard, D., Grima, J.N., Gatt, R.: Auxetic metamaterials exhibiting giant negative Poisson’s ratios. Phys. Status Solidi Rapid Res. Lett. 9, 425–430 (2015). https://doi.org/10.1002/pssr.201510178
Abramovitch, H., Burgard, M., Edery-Azulay, L., Evans, K.E., Hoffmeister, M., Miller, W., et al.: Smart tetrachiral and hexachiral honeycomb: sensing and impact detection. Compos. Sci. Technol. 70, 1072–1079 (2010). https://doi.org/10.1016/j.compscitech.2009.07.017
Jacobs, S., Coconnier, C., Dimaio, D., Scarpa, F., Toso, M., Martinez, J.: Deployable auxetic shape memory alloy cellular antenna demonstrator: design, manufacturing and modal testing. Smart Mater. Struct. (2012). https://doi.org/10.1088/0964-1726/21/7/075013
Scarpa, F., Jacobs, S., Coconnier, C., Toso, M., Di Maio, D.: Auxetic shape memory alloy cellular structures for deployable satellite antennas: design, manufacture and testing. EPJ Web Conf. 6, 27001 (2010). https://doi.org/10.1051/epjconf/20100627001
Airoldi, A., Bettini, P., Panichelli, P., Oktem, M.F., Sala, G.: Chiral topologies for composite morphing structures—Part I: development of a chiral rib for deformable airfoils. Phys. Status Solidi Basic Res. 252, 1435–1445 (2015). https://doi.org/10.1002/pssb.201451689
Olympio, K.R., Gandhi, F.: Zero Poisson’s ratio cellular honeycombs for flex skins undergoing one-dimensional morphing. J. Intell. Mater. Syst. Struct. 21, 1737–1753 (2010)
Spadoni, A., Ruzzene, M.: Static aeroelastic response of chiral-core airfoils. J. Intell. Mater. Syst. Struct. 18, 1067–1075 (2007). https://doi.org/10.1177/1045389X06072361
Airoldi, A., Bettini, P., Panichelli, P., Sala, G.: Chiral topologies for composite morphing structures—Part II: novel configurations and technological processes. Phys. Status Solidi Basic Res. 252, 1446–1454 (2015). https://doi.org/10.1002/pssb.201584263
Crumm, A.T., Halloran, Æ.J.W.: Negative Poisson’ s ratio structures produced from zirconia and nickel using co-extrusion 1336–1342 (2007). https://doi.org/10.1007/s10853-006-1209-y
Schwerdtfeger, J., Heinl, P., Singer, R.F., Korner, C.: Auxetic cellular structures through selective electron-beam melting. Phys. Status Solidi 247, 269–272 (2010). https://doi.org/10.1002/pssb.200945513
Hengsbach, S., Lantada, A.D.: Direct laser writing of auxetic structures: present capabilities and challenges. Smart Mater. Struct. 23, 085033 (2014)
Ren, X., Shen, J., Ghaedizadeh, A., Tian, H., Xie, Y.M.: Experiments and parametric studies on 3D metallic auxetic metamaterials with tuneable mechanical properties. Smart Mater. Struct. 24, 095016 (2015). https://doi.org/10.1088/0964-1726/24/9/095016
Bückmann, T., Stenger, N., Kadic, M., Kaschke, J., Frölich, A., Kennerknecht, T., et al.: Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography. Adv. Mater. (2012). https://doi.org/10.1002/adma.201200584
Babaee, S., Shim, J., Weaver, J.C., Chen, E.R.: Patel N. 3D Soft Metamaterials with Negative Poisson’ s Ratio (2013). https://doi.org/10.1002/adma.201301986
Mizzi, L., Mahdi, E.M., Titov, K., Gatt, R., Attard, D., Evans, K.E., et al.: Mechanical metamaterials with star-shaped pores exhibiting negative and zero Poisson’s ratio. Mater. Des. 146, 28–37 (2018). https://doi.org/10.1016/j.matdes.2018.02.051
Hohmann, J.K., Renner, M., Waller, E.H., von Freymann, G.: Three-dimensional u-printing: an enabling technology. Adv. Opt. Mater. 3, 1488–1507 (2015)
Meza, L.R., Zelhofer, A.J., Clarke, N., Mateos, A.J., Kochmann, D.M., Greer, J.R.: Resilient 3D hierarchical architected metamaterials. Proc. Natl. Acad. Sci. 112, 11502–11507 (2015). https://doi.org/10.1073/pnas.1509120112
Zheng, X., Smith, W., Jackson, J., Moran, B., Cui, H., Chen, D., et al.: Multiscale metallic metamaterials. Nat. Mater. 15, 1100–1107 (2016). https://doi.org/10.1038/NMAT4694
Clausen, A., Wang, F., Jensen, J.S., Sigmund, O., Lewis, J.A.: Topology optimized architectures with programmable Poisson’s ratio over large deformations. Adv. Mater. 27, 5523–5527 (2015). https://doi.org/10.1002/adma.201502485
Ling, B., Wei, K., Wang, Z., Yang, X., Qu, Z., Fang, D.: Experimentally program large magnitude of Poisson’s ratio in additively manufactured mechanical metamaterials. Int. J. Mech. Sci. 173, 105466 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105466
Dudek, K.K., Attard, D., Gatt, R., Grima-Cornish, J.N., Grima, J.N.: The multidirectional auxeticity and negative linear compressibility of a 3D mechanical metamaterial. Mater. Basel 13, 1–16 (2020). https://doi.org/10.3390/ma13092193
Grima, J.N., Gatt, R.: Perforated sheets exhibiting negative Poisson’s ratios. Adv. Eng. Mater. 12, 460–464 (2010). https://doi.org/10.1002/adem.201000005
Grima, J.N., Gatt, R., Ellul, B., Chetcuti, E.: Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations. J. Non Cryst. Solids 356, 1980–1987 (2010). https://doi.org/10.1016/j.jnoncrysol.2010.05.074
Bertoldi, B.K., Reis, P.M., Willshaw, S., Mullin, T.: Negative Poisson’ s ratio behavior induced by an elastic instability. Adv. Funct. Mater. (2009). https://doi.org/10.1002/adma.200901956
Shim, J., Shan, S., Košmrlj, A., Kang, S.H., Chen, E.R., Weaver, J.C., et al.: Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials. Soft Matter 9, 8198–8202 (2013). https://doi.org/10.1039/c3sm51148k
Shen, J., Zhou, S., Huang, X., Xie, Y.M.: Simple cubic three-dimensional auxetic metamaterials. Phys. Status Solidi B Basic Res. 8, 1–8 (2014). https://doi.org/10.1002/pssb.201451304
Slann, A., White, W., Scarpa, F., Boba, K., Farrow, I.: Cellular plates with auxetic rectangular perforations. Phys. Status Solidi 252, 1533–1539 (2015). https://doi.org/10.1002/pssb.201451740
Cho, Y., Shin, J., Costa, A., Ann, T., Kunin, V., Li, J., et al.: Engineering the shape and structure of materials by fractal cut. Proc. Natl. Acad. Sci. 111, 17390–17395 (2014). https://doi.org/10.1073/pnas.1417276111
Tang, Y., Lin, G., Han, L., Qiu, S., Yang, S., Yin, J.: Design of hierarchically cut hinges for highly stretchable and reconfigurable metamaterials with enhanced strength. Adv. Mater. (2015). https://doi.org/10.1002/adma.201502559
Tang, Y., Yin, J.: Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility. Extrem. Mech. Lett. 12, 77–85 (2017). https://doi.org/10.1016/j.eml.2016.07.005
Shan, S., Kang, S.H., Zhao, Z., Fang, L., Bertoldi, K.: Design of planar isotropic negative Poisson’s ratio structures. Extrem. Mech. Lett. 4, 96–102 (2015). https://doi.org/10.1016/j.eml.2015.05.002
Taylor, M., Francesconi, L., Gerendás, M., Shanian, A., Carson, C., Bertoldi, K.: Low porosity metallic periodic structures with negative Poisson’s ratio. Adv. Mater. 26, 2365–2370 (2014)
Mizzi, L., Grima, J.N., Gatt, R., Attard, D.: Analysis of the deformation behavior and mechanical properties of slit-perforated auxetic metamaterials. Phys. Status Solidi (2019). https://doi.org/10.1002/pssb.201800153
Wu, G., Cho, Y., Choi, I., Ge, D., Li, J., Han, H.N., et al.: Directing the deformation paths of soft metamaterials with prescribed asymmetric units. Adv. Mater. (2015). https://doi.org/10.1002/adma.201500716
Mizzi, L., Salvati, E., Spaggiari, A., Tan, J., Korsunsky, A.M.: Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting. Int. J. Mech. Sci. 167, 105242 (2020). https://doi.org/10.1016/j.ijmecsci.2019.105242
Wang, G., Sun, S., Li, M., Zhou, J.: Large deformation shape optimization of cut-mediated soft mechanical metamaterials. Mater. Res. Express 6, 055802 (2019)
Grima, J.N., Mizzi, L., Azzopardi, K.M., Gatt, R.: Auxetic perforated mechanical metamaterials with randomly oriented cuts. Adv. Mater. 28, 385–389 (2016). https://doi.org/10.1002/adma.201503653
Overvelde, J.T.B., Bertoldi, K.: Relating pore shape to the non-linear response of periodic elastomeric structures. J. Mech. Phys. Solids 64, 351–366 (2014). https://doi.org/10.1016/j.jmps.2013.11.014
Rafsanjani, A., Pasini, D.: Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs. Extrem. Mech. Lett. 9, 291–296 (2016)
Jin, L., Khajehtourian, R., Mueller, J., Rafsanjani, A., Tournat, V., Bertoldi, K., et al.: Guided transition waves in multistable mechanical metamaterials. Proc. Natl. Acad. Sci. 117, 2319–2325 (2020)
Grima, J.N., Evans, K.E.: Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 19, 1563–1565 (2000)
Grima, J.N., Evans, K.E.: Auxetic behaviour from rotating triangles. J. Mater. Sci. 41, 3193–3196 (2006)
Attard, D., Grima, J.N.: A three-dimensional rotating rigid units network exhibiting negative Poisson’s ratios. Phys. Status Solidi 249, 1330–1338 (2012)
Grima, J.N., Alderson, A., Evans, K.E.: Negative Poisson’s ratios from rotating rectangles. Comput. Methods Sci. Technol. 10, 137–145 (2004)
Grima, J.N., Alderson, A., Evans, K.E.: Auxetic behaviour from rotating rigid units. Phys. Status Solidi 575, 561–575 (2005). https://doi.org/10.1002/pssb.200460376
Grima, J.N., Gatt, R., Alderson, A., Evans, K.E.: On the auxetic properties of ‘rotating rectangles’ with different connectivity. J. Phys. Soc. Jpn. 74, 2866–2867 (2005)
Grima, J.N., Farrugia, P.-S., Gatt, R., Attard, D.: On the auxetic properties of rotating rhombi and parallelograms: a preliminary investigation. Phys. Status Solidi 245, 521–529 (2008)
Attard, D., Grima, J.N.: Auxetic behaviour from rotating rhombi. Phys. Status Solidi 245, 2395–2404 (2008). https://doi.org/10.1002/pssb.200880269
Attard, D., Manicaro, E., Grima, J.N.: On rotating rigid parallelograms and their potential for exhibiting auxetic behaviour. Phys. Status Solidi B 2044, 2033–2044 (2009). https://doi.org/10.1002/pssb.200982034
Taylor, M., Francesconi, L., Gerendás, M., Shanian, A., Carson, C.: Low porosity metallic periodic structures with negative Poisson’ s ratio. Adv. Mater. (2013). https://doi.org/10.1002/adma.201304464
ANSYS® Academic Research Mechanical, Release 13.0 n.d
Mizzi, L., Attard, D., Gatt, R., Dudek, K.K., Ellul, B., Grima, J.N.: Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis. Eng. Comput. (2020). https://doi.org/10.1007/s00366-019-00910-1
Smith, C.W., Wooton, R.J., Evans, K.E.: Interpretation of experimental data for Poisson’s ratio of highly nonlinear materials. Exp. Mech. 39, 356–362 (1999)
Grima, J.N., Winczewski, S., Mizzi, L., Grech, M.C., Cauchi, R., Gatt, R., et al.: Tailoring graphene to achieve negative Poisson’s ratio properties. Adv. Mater. 27, 1455–1459 (2015). https://doi.org/10.1002/adma.201404106
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Mizzi, L., Attard, D., Evans, K.E. et al. Auxetic mechanical metamaterials with diamond and elliptically shaped perforations. Acta Mech 232, 779–791 (2021). https://doi.org/10.1007/s00707-020-02881-7
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DOI: https://doi.org/10.1007/s00707-020-02881-7