Skip to main content
SpringerLink
Log in

Analyses of mechanically-assembled 3D spiral mesostructures with applications as tunable inductors

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Mechanically-guided assembly allows the formation of 3D spiral-shaped inductors through controlled buckling, which could provide an increased quality (Q) factor and broadened working angle in near field communication, as compared to the planar design. An understanding of the microstructure-property relationship is essential in the design optimization of the assembly process. This work presents a theoretical model to analyze the deformations during the assembly of the 3D spiral-shaped mesostructure from a bilayer precursor that consists of a supporting ribbon and a 2D coil on its top. As validated by both the experiments and finite element analyses (FEA), this mechanics model allows accurate predictions of the assembled 3D configurations. In combination of electromagnetic simulations, we investigated the effects of various key design parameters on the final 3D configuration and the Q factor when operated as an inductor. The results suggest a significant role of the gravity effect on the assembled spiral configuration, especially for flexible coil designs with relative small cross-sectional areas or long wires. This study can serve as a reference for the design of spiral-shaped 3D inductors in different device applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pandey S, Ewing M, Kunas A, et al. Algorithmic design of selffolding polyhedra. Proc Natl Acad Sci USA, 2011, 108: 19885–19890

    Article  Google Scholar 

  2. Yang S, Choi I S, Kamien R D. Design of super-conformable, foldable materials via fractal cuts and lattice kirigami. MRS Bull, 2016, 41: 130–138

    Article  Google Scholar 

  3. Xu L, Shyu T C, Kotov N A. Origami and kirigami nanocomposites. ACS Nano, 2017, 11: 7587–7599

    Article  Google Scholar 

  4. Onal C D, Wood R J, Rus D. An origami-inspired approach to worm robots. IEEE/ASME Trans Mechatron, 2013, 18: 430–438

    Article  Google Scholar 

  5. Zhao Z, Wu J, Mu X, et al. Origami by frontal photopolymerization. Sci Adv, 2017, 3: e1602326

    Article  Google Scholar 

  6. Chen Z, Huang G, Trase I, et al. Mechanical self-assembly of a strainengineered flexible layer: Wrinkling, rolling, and twisting. Phys Rev Appl, 2016, 5: 017001

    Article  Google Scholar 

  7. Schmidt O G, Eberl K. Thin solid films roll up into nanotubes. Nature, 2001, 410: 168

    Article  Google Scholar 

  8. Mei Y, Huang G, Solovev A A, et al. Versatile approach for integrative and functionalized tubes by strain engineering of nanomembranes on polymers. Adv Mater, 2008, 20: 4085–4090

    Article  Google Scholar 

  9. Py C, Reverdy P, Doppler L, et al. Capillary origami: Spontaneous wrapping of a droplet with an elastic sheet. Phys Rev Lett, 2007, 98: 156103

    Article  Google Scholar 

  10. Li H, Guo X, Nuzzo R G, et al. Capillary induced self-assembly of thin foils into 3D structures. J Mech Phys Solids, 2010, 58: 2033–2042

    Article  MATH  Google Scholar 

  11. Na J H, Evans A A, Bae J, et al. Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers. Adv Mater, 2015, 27: 79–85

    Article  Google Scholar 

  12. Yan Z, Zhang F, Wang J, et al. Controlled mechanical buckling for origami-inspired construction of 3D microstructures in advanced materials. Adv Funct Mater, 2016, 26: 2629–2639

    Article  Google Scholar 

  13. Shi Y, Zhang F, Nan K, et al. Plasticity-induced origami for assembly of three dimensional metallic structures guided by compressive buckling. Extreme Mech Lett, 2017, 11: 105–110

    Article  Google Scholar 

  14. Xu S, Yan Z, Jang K I, et al. Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science, 2015, 347: 154–159

    Article  Google Scholar 

  15. Yan Z, Zhang F, Liu F, et al. Mechanical assembly of complex, 3D mesostructures from releasable multilayers of advanced materials. Sci Adv, 2016, 2: e1601014

    Article  Google Scholar 

  16. Zhang Y, Yan Z, Nan K, et al. A mechanically driven form of Kirigami as a route to 3D mesostructures in micro/nanomembranes. Proc Natl Acad Sci USA, 2015, 112: 11757–11764

    Article  Google Scholar 

  17. Fu H, Nan K, Bai W, et al. Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nat Mater, 2018, 17: 268–276

    Article  Google Scholar 

  18. Yan Z, Han M, Shi Y, et al. Three-dimensional mesostructures as high-temperature growth templates, electronic cellular scaffolds, and self-propelled microrobots. Proc Natl Acad Sci USA, 2017, 114: E9455–E9464

    Article  Google Scholar 

  19. Zhang F, Fan Z, Zhang Y. A theoretical model of postbuckling in straight ribbons with engineered thickness distributions for three-dimensional assembly. Int J Solids Struct, 2018, 147: 254–271

    Article  Google Scholar 

  20. Jang K I, Li K, Chung H U, et al. Self-assembled three dimensional network designs for soft electronics. Nat Commun, 2017, 8: 15894

    Article  Google Scholar 

  21. Guo X, Wang X, Ou D, et al. Controlled mechanical assembly of complex 3D mesostructures and strain sensors by tensile buckling. npj Flex Electron, 2018, 2: 14

    Article  Google Scholar 

  22. Lee W, Liu Y, Lee Y, et al. Two-dimensional materials in functional three-dimensional architectures with applications in photodetection and imaging. Nat Commun, 2018, 9: 1417

    Article  Google Scholar 

  23. Zhang Y, Zhang F, Yan Z, et al. Printing, folding and assembly methods for forming 3D mesostructures in advanced materials. Nat Rev Mater, 2017, 2: 17019

    Article  Google Scholar 

  24. Yan Z, Han M, Yang Y, et al. Deterministic assembly of 3D mesostructures in advanced materials via compressive buckling: A short review of recent progress. Extreme Mech Lett, 2017, 11: 96–104

    Article  Google Scholar 

  25. Rogers J, Huang Y, Schmidt O G, et al. Origami MEMS and NEMS. MRS Bull, 2016, 41: 123–129

    Article  Google Scholar 

  26. Li R, Li M, Su Y, et al. An analytical mechanics model for the islandbridge structure of stretchable electronics. Soft Matter, 2013, 9: 8476–8482

    Article  Google Scholar 

  27. Timoshenko S P, Gere J M. Theory of Elastic Stability. New York: McGraw-Hill, 1961

    Google Scholar 

  28. Song J, Huang Y, Xiao J, et al. Mechanics of noncoplanar mesh design for stretchable electronic circuits. J Appl Phys, 2009, 105: 123516

    Article  Google Scholar 

  29. Starostin E L, van der Heijden G H M. Tension-induced multistability in inextensible helical ribbons. Phys Rev Lett, 2008, 101: 084301

    Article  Google Scholar 

  30. Dias M A, Audoly B. “Wunderlich, Meet Kirchhoff”: A general and unified description of elastic ribbons and thin rods. J Elast, 2015, 119: 49–66

    Article  MathSciNet  MATH  Google Scholar 

  31. Hwang K C, Xue M D, Wen X F, et al. Stresses of thick perforated plates with reinforcement of tubes and their effective elastic constants. J Pressure Vessel Technol, 1992, 114: 271–279

    Article  Google Scholar 

  32. Flügge W. Stresses in Shells. Berlin: Springer-Verlag, 1973

    Google Scholar 

  33. Liu Y, Yan Z, Lin Q, et al. Guided formation of 3D helical mesostructures by mechanical buckling: Analytical modeling and experimental validation. Adv Funct Mater, 2016, 26: 2909–2918

    Article  Google Scholar 

  34. Fan Z, Hwang K C, Rogers J A, et al. A double perturbation method of postbuckling analysis in 2D curved beams for assembly of 3D ribbonshaped structures. J Mech Phys Solids, 2018, 111: 215–238

    Article  MathSciNet  Google Scholar 

  35. Li Y, Zhang J, Xing Y, et al. Thermomechanical analysis of epidermal electronic devices integrated with human skin. J Appl Mech, 2017, 84: 111004

    Article  Google Scholar 

  36. Li Y, Chen J, Xing Y, et al. Thermal management of micro-scale inorganic light-emittng diodes on an orthotropic substrate for biointegrated applications. Sci Rep, 2017, 7: 6638

    Article  Google Scholar 

  37. Ye D, Ding Y, Duan Y, et al. Large-scale direct-writing of aligned nanofibers for flexible electronics. Small, 2018, 14: 1703521

    Article  Google Scholar 

  38. Bian J, Ding Y, Duan Y, et al. Buckling-driven self-assembly of selfsimilar inspired micro/nanofibers for ultra-stretchable electronics. Soft Matter, 2017, 13: 7244–7254

    Article  Google Scholar 

  39. Wang Y, Qiu Y, Ameri S K, et al. Low-cost, µm-thick, tape-free electronic tattoo sensors with minimized motion and sweat artifacts. npj Flex Electron, 2018, 2: 6

    Article  Google Scholar 

  40. Song J, Feng X, Huang Y. Mechanics and thermal management of stretchable inorganic electronics. Nat Sci Rev, 2016, 3: 128–143

    Article  Google Scholar 

  41. Zhu J, Dexheimer M, Cheng H. Reconfigurable systems for multifunctional electronics. npj Flex Electron, 2017, 1: 8

    Article  Google Scholar 

  42. Yang S, Chen Y C, Nicolini L, et al. “Cut-and-paste” manufacture of multiparametric epidermal sensor systems. Adv Mater, 2015, 27: 6423–6430

    Article  Google Scholar 

  43. Choi C, Choi M K, Liu S, et al. Human eye-inspired soft optoelectronic device using high-density MoS2-graphene curved image sensor array. Nat Commun, 2017, 8: 1664

    Article  Google Scholar 

  44. Zhang K, Jung Y H, Mikael S, et al. Origami silicon optoelectronics for hemispherical electronic eye systems. Nat Commun, 2017, 8: 1782

    Article  Google Scholar 

  45. Wang T, Ramnarayanan A, Cheng H. Real time analysis of bioanalytes in healthcare, food, zoology and botany. Sensors, 2018, 18: 5

    Article  Google Scholar 

  46. Cheng H. Inorganic dissolvable electronics: Materials and devices for biomedicine and environment. J Mater Res, 2016, 31: 2549–2570

    Article  Google Scholar 

  47. Huang Y A, Wang Y, Xiao L, et al. Microfluidic serpentine antennas with designed mechanical tunability. Lab Chip, 2014, 14: 4205–4212

    Article  Google Scholar 

  48. Jang K I, Chung H U, Xu S, et al. Soft network composite materials with deterministic and bio-inspired designs. Nat Commun, 2015, 6: 6566

    Article  Google Scholar 

  49. Ma Q, Cheng H, Jang K I, et al. A nonlinear mechanics model of bioinspired hierarchical lattice materials consisting of horseshoe microstructures. J Mech Phys Solids, 2016, 90: 179–202

    Article  MathSciNet  Google Scholar 

  50. Zhang Y, Wang S, Li X, et al. Experimental and theoretical studies of serpentine microstructures bonded to prestrained elastomers for stretchable electronics. Adv Funct Mater, 2014, 24: 2028–2037

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Applied Mechanics of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Fan Zhang, Fei Liu & YiHui Zhang

  2. Center for Flexible Electronics Technology and Center for Mechanics and Materials, Tsinghua University, Beijing, 100084, China

    Fan Zhang, Fei Liu & YiHui Zhang

Authors
  1. Fan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YiHui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to YiHui Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, F., Liu, F. & Zhang, Y. Analyses of mechanically-assembled 3D spiral mesostructures with applications as tunable inductors. Sci. China Technol. Sci. 62, 243–251 (2019). https://doi.org/10.1007/s11431-018-9368-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-018-9368-y

Keywords

Search

Navigation