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Optimal design of chiral metamaterials with prescribed nonlinear properties

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Abstract

In this paper, chiral metamaterials (CMM) were optimized from conceptual design to fine design with the effective elastic constants unchanged under finite strain. First, through calculation and comparison of examples, the unit cell method was selected to compute the effective elastic properties of the periodic chiral metamaterials under finite strain. Secondly, the conceptual design of chiral metamaterials with prescribed Poisson’s ratios under finite strain was realized through density-based and feature-driven topology optimization. Then, the method of moving asymptotes (MMA) was used to solve the optimization problems. Based on the optimal configuration, chiral metamaterials with prescribed Poisson’s ratios and Young’s moduli under finite strain were carefully designed through shape optimization. Genetic algorithm was used to solve the optimization problem. Finally, the optimal models were fabricated by 3D printing. The optimal design was validated by tensile test results, i.e., the designed chiral metamaterials can maintain effective elastic properties under large deformation, and the invariance of the effective elastic properties depends on the nonlinearity of the flexible chiral metamaterials.

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References

  • Airoldi A, Crespi M, Quaranta G et al (2010) Design of a morphing airfoil with composite chiral structure. J Aircr 49:1008–1019

    Google Scholar 

  • Bertoldi K, Reis PM, Willshaw S et al (2010) Negative Poisson’s ratio behavior induced by an elastic instability. Adv Mater 22:361–366

    Google Scholar 

  • Bhullar SK, Mawanane HAT, Alderson A et al (2013) Influence of negative Poisson’s ratio on stent applications. Adv Mater 2:42–47

    Google Scholar 

  • Buhl T, Pedersen CBW, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19:93–104

    Google Scholar 

  • Dale AS, Cooper JE (2014) Topology optimization & experimental validation of 0-υ honeycomb for adaptive morphing wing, 22nd AIAA/ASME/AHS adaptive structures conference. Reston: AIAA Inc 0763:1–10

    Google Scholar 

  • Diaz AR, Sigmund O (2010) A topology optimization method for design of negative permeability metamaterials. Struct Multidiscip Optim 41:163–177

    MathSciNet  MATH  Google Scholar 

  • Dong HW, Wang YS, Zhang C (2017) Topology optimization of chiral phoxonic crystals with simultaneously large phononic and photonic bandgaps. IEEE Photonics J 9:1–16

    Google Scholar 

  • Evans KE, Caddock BD (1989) Microporous materials with negative Poisson’s ratios .2. Mechanisms and interpretation. J Phys D-Appl Phys 22:1883–1887

    Google Scholar 

  • Grima JN, Caruana-Gauci R (2012) Mechanical metamaterials: materials that push back. Nat Mater 11:565–566

    Google Scholar 

  • Hassan, MR, Scarpa, F, Mohamed N A, et al (2008) Tensile properties of shape memory alloy chiral honeycombs, physica status solidi (b), 245:2440–2444

  • Heo H, Ju J, Kim DM (2013) Compliant cellular structures: application to a passive morphing airfoil. Compos Struct 106:560–569

    Google Scholar 

  • Hu N, Wang B, Tan GW (2000) Effective elastic properties of 2-D solids with circular holes: numerical simulations. Compos Sci Technol 60:1811–1823

    Google Scholar 

  • Kim K, Ju J (2015) Mechanical metamaterials with 3D compliant porous structures. Compos Struct 132:874–884

    Google Scholar 

  • Kolken HMA, Zadpoor AA (2017) Auxetic mechanical metamaterials. RSC Adv 7:5111–5129

    Google Scholar 

  • Korner C, Liebold-Ribeiro Y (2015) A systematic approach to identify cellular auxetic materials. Smart Mater Struct 24:025013

    Google Scholar 

  • Kumar D, Wang ZP, Poh LH (2019) Isogeometric shape optimization of smoothed petal auxetics with prescribed nonlinear deformation. Comput Methods Appl Mech Eng 356:16–43

    MathSciNet  MATH  Google Scholar 

  • Meng L, Zhang WH, Quan D et al (2019) From topology optimization design to additive manufacturing: today’s success and tomorrow’s roadmap. Arch Comput Methods Eng 27:805–830

    Google Scholar 

  • Nicolaou ZG, Motter AE (2012) Mechanical metamaterials with negative compressibility transitions. Nat Mater 11:608–613

    Google Scholar 

  • Qiu KP, Wang Z, Zhang WH (2016) The effective elastic properties of flexible hexagonal honeycomb cores with consideration for geometric nonlinearity. Aerosp Sci Technol 58:258–266

    Google Scholar 

  • Qiu KP, Wang RY, Wang Z, Zhang WH (2018) Effective elastic properties of flexible chiral honeycomb cores including geometrically nonlinear effects. Meccanica 53:3661–3672

    MathSciNet  Google Scholar 

  • Radman A, Huang X, Xie Y (2013) Topological optimization for the design of microstructures of isotropic cellular materials. Eng Optim 45:1331–1348

    MathSciNet  Google Scholar 

  • Ren X, Das R, Tran P et al (2018) Auxetic metamaterials and structures: a review. Smart Mater Struct 27:023001

    Google Scholar 

  • Rocklin DZ, Zhou SN, Sun K et al (2017) Transformable topological mechanical metamaterials. Nat Commun 8:14201

    Google Scholar 

  • Schurig D, Mock JJ, Justice BJ et al (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980

    Google Scholar 

  • Sigmund O (1995) Tailoring materials with prescribed elastic properties. Mech Mater 20:351–368

    Google Scholar 

  • Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45:1037–1067

    MathSciNet  Google Scholar 

  • Smith CW, Wootton RJ, Evans KE (1999) Interpretation of experimental data for Poisson’s ratio of highly nonlinear materials. Exp Mech 39:356–362

    Google Scholar 

  • Valentine J, Zhang S, Zentgraf T et al (2008) Three-dimensional optical metamaterial with a negative refractive index. Nature 455:376–379

    Google Scholar 

  • Wang FW (2018) Systematic design of 3D auxetic lattice materials with programmable Poisson’s ratio for finite strains. J Mech Phys Solids 114:303–318

    MathSciNet  Google Scholar 

  • Wang ZP, Poh LH (2018) Optimal form and size characterization of planar isotropic petal-shaped auxetics with tunable effective properties using IGA. Compos Struct 201:486–502

    Google Scholar 

  • Wang F, Sigmund O, Jensen JS (2014a) Design of materials with prescribed nonlinear properties. J Mech Phys Solids 69:156–174

    MathSciNet  Google Scholar 

  • Wang YQ, Luo Z, Zhang N, Kang Z (2014b) Topological shape optimization of microstructural metamaterials using a level set method. Comput Mater Sci 87:178–186

    Google Scholar 

  • Wang K, Chang YH, Chen YW et al (2015) Designable dual-material auxetic metamaterials using three-dimensional printing. Mater Des 67:159–164

    Google Scholar 

  • Wang Q, Jackson JA, Ge Q et al (2016) Lightweight mechanical metamaterials with tunable negative thermal expansion. Phys Rev Lett 117:175901

    Google Scholar 

  • Wang ZP, Poh LH, Dirrenberger J et al (2017) Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization. Comput Methods Appl Mech Eng 323:250–271

    MathSciNet  MATH  Google Scholar 

  • Wang H, Zhang YX, Lin WQ et al (2020) A novel two-dimensional mechanical metamaterial with negative Poisson’s ratio. Comput Mater Sci 171:109232

    Google Scholar 

  • Wu WW, Hu WX, Qian G et al (2019) Mechanical design and multifunctional applications of chiral mechanical metamaterials: a review. Mater Des 180:107950

    Google Scholar 

  • Yang L, Harrysson O, Cormier D et al (2015) Additive manufacturing of metal cellular structures: design and fabrication. JOM 67:608–615

    Google Scholar 

  • Yu XL, Zhou J, Liang HY et al (2018) Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review. Prog Mater Sci 94:114–173

    Google Scholar 

  • Zhang HK, Luo YJ, Kang Z (2018) Bi-material microstructural design of chiral auxetic metamaterials using topology optimization. Compos Struct 195:232–248

    Google Scholar 

  • Zhao JF, Li Y, Liu WK (2015) Predicting band structure of 3D mechanical metamaterials with complex geometry via XFEM. Comput Mech 55:659–672

    MathSciNet  MATH  Google Scholar 

  • Zhou Y, Zhang WH, Zhu JH et al (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1–32

    MathSciNet  MATH  Google Scholar 

  • Zhu YL, Wang ZP, Poh LH (2018) Auxetic hexachiral structures with wavy ligaments for large elasto-plastic deformation. Smart Mater Struct 27:055001

    Google Scholar 

  • Zhu YL, Jiang SH, Poh LH et al (2020) Enhanced hexa-missing rib auxetics for achieving targeted constant NPR and in-plane isotropy at finite deformation. Smart Mater Struct 29:1–14

    Google Scholar 

Download references

Funding

This work is supported by National Key Research and Development Program (2017YFB1102800), NSFC for Excellent Young Scholars (11722219), National Natural Science Foundation of China (11772258, 51790171).

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Correspondence to Kepeng Qiu.

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The authors declare that they have no conflict of interest.

Replication of results

In this work, the main codes of the feature-based design method in the CAD community are available from the authors on reasonable request in the reference (Zhou, Y, Zhang, WH, Zhu, JH, et al. 2016).

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Qiu, K., Wang, R., Xie, Z. et al. Optimal design of chiral metamaterials with prescribed nonlinear properties. Struct Multidisc Optim 63, 595–611 (2021). https://doi.org/10.1007/s00158-020-02747-5

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  • DOI: https://doi.org/10.1007/s00158-020-02747-5

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