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Developing Mechanical Metamaterials Under an Adaptable Topology Optimization Design Framework

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Abstract

Developing mechanical metamaterials through topology optimization attracts high attention in both computational design and engineering applications. However, most of the studies in the literature are of quite limited applicability and poor extensibility. Hence, this work originally established an adaptable metamaterial topology optimization framework through integrating a commercial finite element analysis (FEA) platform. Particularly, the sensitivity analysis was derived and simplified to avoid the complex extraction of internal FEA information according to the strain-energy-based homogenization method. A series of two- and three-dimensional metamaterials with different properties, i.e., bulk and shear moduli, negative Poisson’s ratio, were subsequently devised. These optimized metamaterials were fabricated and experimentally tested based on the additive manufacturing, firmly demonstrating the effectiveness of the developed design framework. This well-structured design framework can be conveniently extended to the systematic design of metamaterials with various other exclusive performances, fulfilling the urgent need for metamaterial design methods.

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All data generated during this study are included in this published paper and related supporting information.

References

  1. Vangelatos Z, Gu GX, Grigoropoulos CP. Architected metamaterials with tailored 3D buckling mechanisms at the microscale. Extreme Mech Lett. 2019;33:100580.

    Article  Google Scholar 

  2. Ling B, Wei K, Qu Z, Fang D. Design and analysis for large magnitudes of programmable Poisson’s ratio in a series of lightweight cylindrical metastructures. Int J Mech Sci. 2021;2021(195):106220.

    Article  Google Scholar 

  3. Wei K, Peng Y, Wang K, Duan S, Yang X, Wen W. Three dimensional lightweight lattice structures with large positive, zero and negative thermal expansion. Compos Struct. 2018;188:287–96.

    Article  Google Scholar 

  4. Liu P, Yan Y, Zhang X, Luo Y, Kang Z. Topological design of microstructures using periodic material-field series-expansion and gradient-free optimization algorithm. Mater Des. 2021;199:109437.

    Article  Google Scholar 

  5. Zhou S, Cadman J, Chen Y, Li W, Xie YM, Huang X, et al. Design and fabrication of biphasic cellular materials with transport properties—a modified bidirectional evolutionary structural optimization procedure and MATLAB program. Int J Heat Mass Transf. 2012;55:8149–62.

    Article  Google Scholar 

  6. Xia L, Breitkopf P. Design of materials using topology optimization and energy-based homogenization approach in Matlab. Struct Multidiscip Optim. 2015;52:1229–41.

    Article  MathSciNet  Google Scholar 

  7. Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O. Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim. 2011;43:1–16.

    Article  MATH  Google Scholar 

  8. Lagaros ND, Vasileiou N, Kazakis G. AC# code for solving 3D topology optimization problems using SAP2000. Optim Eng. 2019;20:1–35.

    Article  MATH  Google Scholar 

  9. Zuo ZH, Xie YM. A simple and compact Python code for complex 3D topology optimization. Adv Eng Softw. 2015;85:1–11.

    Article  Google Scholar 

  10. Chen Q, Zhang X, Zhu B. A 213-line topology optimization code for geometrically nonlinear structures. Struct Multidiscip Optim. 2019;59:1863–79.

    Article  MathSciNet  Google Scholar 

  11. Sigmund O. A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim. 2001;21:120–7.

    Article  Google Scholar 

  12. Bendsoe MP, Sigmund O. Topology optimization: theory, methods, and applications. Berlin: Springer; 2013. p. 16–8.

    Google Scholar 

  13. Suresh K. A 199-line Matlab code for Pareto-optimal tracing in topology optimization. Struct Multidiscip Optim. 2010;42:665–79.

    Article  MathSciNet  MATH  Google Scholar 

  14. Schmidt S, Schulz V. A 2589 line topology optimization code written for the graphics card. Comput Vis Sci. 2011;14:249–56.

    Article  MathSciNet  MATH  Google Scholar 

  15. Talischi C, Paulino GH, Pereira A, Menezes IF. PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Struct Multidiscip Optim. 2012;45:329–57.

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu K, Tovar A. An efficient 3D topology optimization code written in Matlab. Struct Multidiscip Optim. 2014;50:1175–96.

    Article  MathSciNet  Google Scholar 

  17. Tavakoli R, Mohseni SM. Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation. Struct Multidiscip Optim. 2014;49:621–42.

    Article  MathSciNet  Google Scholar 

  18. Huang X, Xie M. Evolutionary topology optimization of continuum structures: methods and applications. New York: Wiley; 2010. p. 110–2.

    Book  MATH  Google Scholar 

  19. Wang S, Wang MY. Radial basis functions and level set method for structural topology optimization. Int J Numer Meth Eng. 2006;65:2060–90.

    Article  MathSciNet  MATH  Google Scholar 

  20. Challis VJ. A discrete level-set topology optimization code written in Matlab. Struct Multidiscip Optim. 2010;41:453–64.

    Article  MathSciNet  MATH  Google Scholar 

  21. Otomori M, Yamada T, Izui K, Nishiwaki S. Matlab code for a level set-based topology optimization method using a reaction diffusion equation. Struct Multidiscip Optim. 2015;51:1159–72.

    Article  MathSciNet  Google Scholar 

  22. Wei P, Li Z, Li X, Wang MY. An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Struct Multidiscip Optim. 2018;58:831–49.

    Article  MathSciNet  Google Scholar 

  23. Olesen LH, Okkels F, Bruus H. A high-level programming-language implementation of topology optimization applied to steady-state Navier–Stokes flow. Int J Numer Meth Eng. 2006;65:975–1001.

    Article  MathSciNet  MATH  Google Scholar 

  24. Zegard T, Paulino GH. GRAND3—ground structure based topology optimization for arbitrary 3D domains using MATLAB. Struct Multidiscip Optim. 2015;52:1161–84.

    Article  Google Scholar 

  25. Sun Z, Li D, Zhang W, Shi S, Guo X. Topological optimization of biomimetic sandwich structures with hybrid core and CFRP face sheets. Compos Sci Technol. 2017;142:79–90.

    Article  Google Scholar 

  26. Zhang W, Yuan J, Zhang J, Guo X. A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim. 2016;53:1243–60.

    Article  MathSciNet  Google Scholar 

  27. Sun Z, Cui R, Cui T, Liu C, Shi S, Guo X. An optimization approach for stiffener layout of composite stiffened panels based on moving morphable components (MMCs). Acta Mech Solida Sin. 2020;33:650–62.

    Article  Google Scholar 

  28. Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Arch Appl Mech. 1999;69:635–54.

    Article  MATH  Google Scholar 

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Funding

This research was supported by the Science and Technology Innovation Program of Hunan Province under grant #2021RC30306, Natural Science Foundation of Hunan Province under grant #2021JJ30085, the fund of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body under Grant #52,175,012, and the Open Research Fund of State Key Laboratory of High Performance Complex Manufacturing, Central South University under Grant # Kfkt2021-01.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Zhengtong Han, Kai Wei, Xiaoyang Liu, Yuhang Long, Jialong Li & Xinglin Chen

  2. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, China

    Kai Wei

Authors
  1. Zhengtong Han
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  2. Kai Wei
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  3. Xiaoyang Liu
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  4. Yuhang Long
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  5. Jialong Li
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Contributions

Zhengtong Han provided all the data for this paper and was a major contributor in writing this paper; Xiaoyang Liua, Yuhang Longa, Jialong Lia and Xinglin Chen made great contributions to the revision of this paper; Kai Wei conceived the main idea of this paper and also put forward valuable suggestions for the revision of this paper. All authors read and approved the final manuscript.

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Correspondence to Kai Wei.

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Han, Z., Wei, K., Liu, X. et al. Developing Mechanical Metamaterials Under an Adaptable Topology Optimization Design Framework. Acta Mech. Solida Sin. 36, 306–316 (2023). https://doi.org/10.1007/s10338-023-00379-y

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  • DOI: https://doi.org/10.1007/s10338-023-00379-y

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