Journal of Materials Science

, Volume 48, Issue 24, pp 8443–8448 | Cite as

Design of two-dimensional horseshoe layout for stretchable electronic systems



Using appropriate layout in the design of the stretchable electronics is very important, since the optimized layout is capable of making the electronic system stretchable and maintaining the electrical performance and structural reliability. In this paper, a unit cell model with periodic boundary condition is proposed to investigate the stretchability and optimize the structure of the stretchable electronic systems with the 2D “horseshoe” layout. Unlike the monotonous trends in the cases of the “wavy”, “mesh”, and 1D “horseshoe” layout, each impact factor (metal wire thickness, metal wire width, eccentric angle) has an optimized value for the stretchability to reach its maximum. To comprehensively investigate the influence of these impact factors on the stretchability, we employ the response surface method and obtain the quadratic response surface function to mathematically explore the relationship between these impact factors and the stretchability of interest. The response surface method proposes an optimal design of the 2D “horseshoe” layout for the maximum stretchability, which agrees well with the finite element simulations results. The findings here provide a more programmable scheme and can be useful in formulating designs for the stretchable electronic systems.


Shape Transition Maximum Strain Response Surface Method Metal Wire Tensile Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge the support from the Key Project of Chinese National Programs for Fundamental Research and Development (2010CB832703, 2014CB049000) and Natural Science Foundation of China (91130025). M. Li would also acknowledge the support by the Fundamental Research Funds for the Central Universities and China Postdoctoral Science Foundation (2013M530907).


  1. 1.
    Rogers JA, Someya T, Huang YG (2010) Science 327:1603CrossRefGoogle Scholar
  2. 2.
    Rogers JA, Bao Z, Baldwin K et al (2001) Proc Natl Acad Sci USA 98:4835CrossRefGoogle Scholar
  3. 3.
    Gelinck GH, Huitema HEA, van Veenendaal E et al (2004) Nat Mater 3:106CrossRefGoogle Scholar
  4. 4.
    Jung I, Xiao J, Malyarchuk V et al (2011) Proc Natl Acad Sci USA 108:1788CrossRefGoogle Scholar
  5. 5.
    Ko HC, Stoykovich MP, Song J et al (2008) Nature 454:748CrossRefGoogle Scholar
  6. 6.
    Lee J, Wu J, Shi M et al (2011) Adv Mater 23:986CrossRefGoogle Scholar
  7. 7.
    Kim DH, Lu N, Ma R et al (2011) Science 333:838CrossRefGoogle Scholar
  8. 8.
    Kim DH, Viventi J, Amsden JJ et al (2010) Nat Mater 9:511CrossRefGoogle Scholar
  9. 9.
    Song J, Jiang H, Choi WM et al (2008) J Appl Phys 103:014303CrossRefGoogle Scholar
  10. 10.
    Song J, Huang Y, Xiao J et al (2009) J Appl Phys 105:123516CrossRefGoogle Scholar
  11. 11.
    Gonzalez M, Axisa F, Bulcke MV et al (2008) Microelectron Reliab 48:825CrossRefGoogle Scholar
  12. 12.
    Yu C, Duan Z, Yuan P et al (2013) Adv Mater 25:1541CrossRefGoogle Scholar
  13. 13.
    Wang SD, Song JZ, Kim DH et al (2008) Appl Phys Lett 93:023126CrossRefGoogle Scholar
  14. 14.
    Su Y, Wu J, Fan Z et al (2012) J Mech Phys Solids 60:487CrossRefGoogle Scholar
  15. 15.
    Khang DY, Jiang HQ, Huang Y et al (2006) Science 311:208CrossRefGoogle Scholar
  16. 16.
    Jiang HQ, Khang DY, Song JZ et al (2007) Proc Natl Acad Sci USA 104:15607CrossRefGoogle Scholar
  17. 17.
    Song J, Jiang H, Liu ZJ et al (2008) Int J Solids Struct 45:3107CrossRefGoogle Scholar
  18. 18.
    Koh CT, Liu ZJ, Khang DY et al (2007) Appl Phys Lett 91:133113CrossRefGoogle Scholar
  19. 19.
    Jiang HQ, Khang DY, Fei HY et al (2008) J Mech Phys Solids 56:2585CrossRefGoogle Scholar
  20. 20.
    ABAQUS Analysis User’s Manual V6.9 (Dassault Systemes, Pawtucket, RI, 2009)Google Scholar
  21. 21.
    Lacour SP, Wagner S, Huang ZY et al (2003) Appl Phys Lett 82:2404CrossRefGoogle Scholar
  22. 22.
    Hill WJ, Hunter WG (1966) Technometrics 8:571CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  2. 2.Department of Mechanical Engineering and Department of Civil and Environmental EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations