Acta Mechanica Solida Sinica

, Volume 23, Issue 6, pp 592–599 | Cite as

Mechanics analysis of two-dimensionally prestrained elastomeric thin film for stretchable electronics

  • Ming Li
  • Jianliang Xiao
  • Jian Wu
  • Rak-Hwan Kim
  • Zhan Kang
  • Yonggang Huang
  • John A. Rogers


Various methods have been developed to fabricate highly stretchable electronics. Recent studies show that over 100% two dimensional stretchability can be achieved by mesh structure of brittle functioning devices interconnected with serpentine bridges. Kim et al show that pressing down an inflated elastomeric thin film during transfer printing introduces two dimensional prestrain, and therefore further improves the system stretchability. This paper gives a theoretical study of this process, through both analytical and numerical approaches. Simple analytical solutions are obtained for meridional and circumferential strains in the thin film, as well as the maximum strain in device islands, which all agree reasonably well with finite element analysis.

Key words

stretchable electronics shell soft materials 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kim, D.H., Ahn, J.H., Choi, W.M., Kim, H.S., Kim, T.H., Song, J., Huang, Y., Liu, Z., Lu, C. and Rogers, J.A., Stretchable and foldable silicon integrated circuits. Science, 2008, 320: 507–511.CrossRefGoogle Scholar
  2. [2]
    Kim, D.H., Choi, W.M., Ahn, J.H., Kim, H.S., Song, J., Huang, Y., Liu, Z., Lu, C., Koh, C.G. and Rogers, J.A., Complementary metal oxide silicon integrated circuits incorporating monolithically integrated stretchable wavy interconnects. Applied Physics Letters, 2008, 93: 044102.CrossRefGoogle Scholar
  3. [3]
    Kim, D.H., Liu, Z., Kim, Y.S., Wu, J., Song, J., Kim, H.S., Huang, Y., Hwang, K.C., Zhang, Y. and Rogers, J.A., Optimized structural designs for stretchable silicon integrated circuits. Small, 2009, 5: 2841–2847.CrossRefGoogle Scholar
  4. [4]
    Kim, D.H., Viventi, J., Amsden, J.J., Xiao, J., Vigeland, L., Kim, Y.S., Blanco, J.A., Panilaitis, B., Frechette, E.S., Contreras, D., Kaplan, D.L., Omenetto, F.G., Huang, Y., Hwang, K.C., Zakin, M.R., Litt, B. and Rogers, J.A., Dissolvable films of silk fibroin for ultrathin conformal bio-integrated electronics. Nature Materials, 2010, 9: 511–517.CrossRefGoogle Scholar
  5. [5]
    Viventi, J., Kim, D.H., Moss, J.D., Kim, Y.S., Blanco, J.A., Annetta, N., Hicks, A., Xiao, J., Huang, Y., Callans, D.J., Rogers, J.A. and Litt, B., A conformal, bio-interfaced class of silicon electronics for mapping cardiac electrophysiology. Science Translational Medicine, 2010, 2: 24ra22.CrossRefGoogle Scholar
  6. [6]
    Mannsfeld, S.C.B., Tee, B.C.K., Stoltenberg, R.M., Chen, C.V.H.H., Barman, S., Muir, B.V.O., Sokolov, A.N., Reese, C. and Bao, Z., Highly sensitive flexible pressure sensors with microstructured rubber dielectric layers. Nature Materials, 2010, 9: 859–864.CrossRefGoogle Scholar
  7. [7]
    Takei, K., Takahashi, T., Ho, J.C., Ko, H., Gillies, A.G., Leu, P.W., Fearing, R.S. and Javey, A., Nanowire active-matrix circuitry for low-voltage macroscale artificial skin. Nature Materials, 2010, 9: 821–826.CrossRefGoogle Scholar
  8. [8]
    Someya, T., Sakurai, T., Sekitani, T. and Noguchi, Y., Printed organic transistors for large-area electronics. In: 6th International Conference on Polymers and Adhesives in Microelectronics and Photonics, 2007: 6–11.Google Scholar
  9. [9]
    Kim, R.H., Kim, D.H., Xiao, J., Kim, B.H., Park, S.I., Panilaitis, B., Ghaffari, R., Yao, J., Li, M., Liu, Z., Malyarchuk, V., Kim, D.G., Le., A.P., Nuzzo, G., R., Kaplan., D.L., Omenetto., F.G., Huang, Y., Kang, Z. and Rogers, J.A., Waterproof AlInGaP optoelectronics on flexible substrates with applications in biomedicine and robotics. Nature Materials, 2010, 9: 929–937.CrossRefGoogle Scholar
  10. [10]
    Bernards, D.A., Biegala, T., Samuels, Z.A., Slinker, J.D., Malliaras, G.G., Flores-Torres, S., Abruna, H.D. and Rogers, J.A., Organic light-emitting devices with laminated top contacts. Applied Physics Letters, 2004, 84: 3675–3677.CrossRefGoogle Scholar
  11. [11]
    Park, S.I., Le, A.P., Wu, J., Huang, Y., Li, X. and Rogers, J.A., Light emission characteristics and mechanics of foldable inorganic light-emitting diodes. Advanced Materials, 2010, 22: 3062–3066.CrossRefGoogle Scholar
  12. [12]
    Lee, T.W., Zaumseil, J., Bao, Z., Hsu, J.W.P. and Rogers, J.A., Organic light-emitting diodes formed by soft contact lamination. Proceedings of the National Academy of Sciences of the United States of America, 2004, 101: 429–433.CrossRefGoogle Scholar
  13. [13]
    Park, S.I., Xiong, Y., Kim, R.H., Elvikis, P., Meitl, M., Kim, D.H., Wu, J., Yoon, J., Yu, C.J., Liu, Z., Huang, Y., Hwang, K.C., Ferreira, P., Li, X., Choquette, K. and Rogers, J.A., Printed assemblies of inorganic light-emitting diodes for deformable and semitransparent displays. Science, 2009, 325: 977–981.CrossRefGoogle Scholar
  14. [14]
    Rogers, J.A., Bao, Z., Baldwin, K., Dodabalapur, A., Crone, B., Raju, V.R., Kuck, V., Katz, H., Amundson, K., Ewing, J. and Drzaic, P., Paper-like electronic displays: Large-area rubber-stamped plastic sheets of electronics and microencapsulated electrophoretic inks. Proceedings of the National Academy of Sciences of the United States of America, 2001, 98: 4835–4840.CrossRefGoogle Scholar
  15. [15]
    Jung, I., Shin, G., Malyarchuk, V., Ha, J.S. and Rogers, J.A., Paraboloid electronic eye cameras using deformable arrays of photodetectors in hexagonal mesh layouts. Applied Physics Letters, 2010, 96: 021110.CrossRefGoogle Scholar
  16. [16]
    Wang, S., Xiao, J., Jung, I., Song, J., Ko, H.C., Stoykovich, M.P., Huang, Y., Hwang, K.C. and Rogers, J.A., Mechanics of hemispherical electronics. Applied Physics Letters, 2009, 95: 181912.CrossRefGoogle Scholar
  17. [17]
    Ko, H.C., Stoykovich, M.P., Song, J., Malyarchuk, V., Choi, W.M., Yu, C.J., Geddes, J.B., Xiao, J., Wang, S., Huang, Y. and Rogers, J.A., A hemispherical electronic eye camera based on compressible silicon optoelectronics. Nature, 2008, 454: 748–753.CrossRefGoogle Scholar
  18. [18]
    Ko, H.C., Shin, G., Wang, S., Stoykovich, M.P., Lee, J.W., Kim, D.H., Ha, J.S., Huang, Y., Hwang, K.C. and Rogers, J.A., Curvilinear electronics formed using silicon membrane circuits and elastomeric transfer elements. Small, 2009, 5: 2703–2709.CrossRefGoogle Scholar
  19. [19]
    Shin, G., Jung, I., Malyarchuk, V., Song, J., Wang, S., Ko, H.C., Huang, Y., Ha, J.S. and Rogers, J.A., Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic eye cameras. Small, 2010, 6: 851–856.CrossRefGoogle Scholar
  20. [20]
    Kim, D.H., Xiao, J., Song, J., Huang, Y. and Rogers, J.A., Stretchable, curvilinear electronics based on inorganic materials. Advanced Materials, 2010, 22: 2108–2124.CrossRefGoogle Scholar
  21. [21]
    Wang, S., Xiao, J., Song, J., Ko, H.C., Hwang, K.C., Huang, Y. and Rogers, J.A., Mechanics of curvilinear electronics. Soft Matter, 2010, 6: 5757–5763.CrossRefGoogle Scholar
  22. [22]
    Yoon, J., Baca, A.J., Park, S.I., Elvikis, P., Geddes, J.B., Li, L., Kim, R.H., Xiao, J., Wang, S., Kim, T.H., Motala, M.J., Ahn, B.Y., Duoss, E.B., Lewis, J.A., Nuzzo, R.G., Ferreira, P.M., Huang, Y., Rockett, A. and Rogers, J.A., Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs. Nature Materials, 2008, 7: 907–915.CrossRefGoogle Scholar
  23. [23]
    Baca, A.J., Yu, K.J., Xiao, J., Wang, S., Yoon, J., Ryu, J.H., Stevenson, D., Nuzzo, R.G., Rockett, A.A., Huang, Y. and Rogers, J.A., Compact monocrystalline silicon solar modules with high voltage outputs and mechanically flexible designs. Energy Environmental Science, 2010, 3: 208–211.CrossRefGoogle Scholar
  24. [24]
    Rogers, J.A. and Huang, Y., A curvy, stretchy future for electronics. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106: 10875–10876.CrossRefGoogle Scholar
  25. [25]
    Rogers, J.A., Someya, T. and Huang, Y., Materials and mechanics for stretchable electronics. Science, 2010, 327: 1603–1607.CrossRefGoogle Scholar
  26. [26]
    Khang, D.Y., Jiang, H., Huang, Y. and Rogers, J.A., A stretchable form of single-crystal silicon for highperformance electronics on rubber substrates. Science, 2006, 311: 208–212.CrossRefGoogle Scholar
  27. [27]
    Jiang, H., Khang, D, Y., Song, J., Sun, Y., Huang, Y. and Rogers, J.A., Finite deformation mechanics in buckled thin films on compliant supports. Proceedings of the National Academy of Sciences of the United States of America, 2007, 104: 15607–15612.CrossRefGoogle Scholar
  28. [28]
    Khang, D.Y., Xiao, J., Kocabas, C., MacLaren, S., Banks, T., Jiang, H., Huang, Y. and Rogers, J.A., Molecular scale buckling mechanics on individual aligned single-wall carbon nanotubes on elastomeric substrates. Nano Letters, 2008, 8: 124–130.CrossRefGoogle Scholar
  29. [29]
    Xiao, J., Jiang, H., Khang, D.Y., Wu, J., Huang, Y. and Rogers, J.A., Mechanics of buckled carbon nanotubes on elastomeric substrates. Journal of Applied Physics, 2008, 104: 033543.CrossRefGoogle Scholar
  30. [30]
    Ryu, S.Y., Xiao, J., Park, W.II., Son, K.S., Huang, Y., Paik, U. and Rogers, J.A., Lateral buckling mechanics in silicon nanowires on elastomeric substrates. Nano Letters, 2009, 9: 3214–3219.CrossRefGoogle Scholar
  31. [31]
    Xiao, J., Ryu, S.Y., Huang, Y., Hwang, K.C., Paik, U. and Rogers, J.A., Mechanics of nanowire/nanotube insurface buckling on elastomeric substrates. Nanotechnology, 2010, 21: 085708.CrossRefGoogle Scholar
  32. [32]
    Lacour, S.P., Chan, D., Wagner, S., Li, T. and Suo, Z., Mechanisms of reversible stretchability of thin metal films on elastomeric substrates. Applied Physics Letters, 2006, 88: 204103.CrossRefGoogle Scholar
  33. [33]
    Lacour, S.P., Wagner, S., Huang, Z. and Suo, Z., Stretchable gold conductors on elastomeric substrates. Applied Physics Letters, 2003, 82: 2404.CrossRefGoogle Scholar
  34. [34]
    Li, T., Suo, Z., Lacour, S.P. and Wagner, S., Compliant thin film patterns of stiff materials as platforms for stretchable electronics. Journal of Materials Research, 2005, 20: 3274–3277.CrossRefGoogle Scholar
  35. [35]
    Li, T., Huang, Z., Suo, Z., Lacour, S.P. and Wagner, S., Stretchability of thin metal films on elastomer substrates. Applied Physics Letters, 2004, 85: 3435–3437.CrossRefGoogle Scholar
  36. [36]
    Mcdonald, J.C. and Whitesides, G.M., Poly (dimethylsiloxane) as a material for fabricating microfluidic devices. Accounts of Chemical Research, 2002, 35: 491–499.CrossRefGoogle Scholar
  37. [37]
    Kmaltezos, G., Nortrup, R., Jeon, S., Zaumseil, J. and Rogers, J.A., Tunable organic transistors that use microfluidic source and drain electrodes. Applied Physics Letters, 2003, 83: 10.Google Scholar
  38. [38]
    Kim, H.J., Son, Ch. and Ziaie B., A multiaxial stretchable interconnect using liquid-alloy-filled elastomeric microchannels. Applied Physics Letters, 2008, 92: 011904.CrossRefGoogle Scholar
  39. [39]
    Choi, W.M., Song, J., Khang, D.Y., Jiang, H., Huang, Y. and Rogers, J.A., Biaxially stretchable ‘Wavy’ silicon nanomembranes. Nano Letters, 2007, 7: 1655–1663.CrossRefGoogle Scholar
  40. [40]
    So, J.H., Thelen, J., Qusba, A., Hayes, G.J., Lazzi, G. and Dickey, M.D., Reversibly deformable and mechanically tunable fluidic antennas. Advanced Functional Materials, 2009, 19: 3632–3637.CrossRefGoogle Scholar
  41. [41]
    Jiang, H., Khang, D.Y., Fei, H., Kim, H., Huang, Y., Xiao, J. and Rogers, J.A., Finite width effect of thin-films buckling on compliant substrate: experimental and theoretical studies. Journal of the Mechanics and Physics of Solids, 2008, 56: 2585–2598.MathSciNetCrossRefGoogle Scholar
  42. [42]
    Wang, S., Song, J., Kim, D.H., Huang, Y. and Rogers, J.A., Local versus global buckling of thin films on elastomeric substrates. Applied Physics Letters, 2008, 93: 023126.CrossRefGoogle Scholar
  43. [43]
    Song, J., Jiang, H., Liu, Z., Khang, D.Y., Huang, Y., Rogers, J.A., Lu, C. and Koh, C.G., Buckling of a stiff thin film on a compliant substrate in large deformation. International Journal of Solids and Structures, 2008, 45: 3107–3121.CrossRefGoogle Scholar
  44. [44]
    Siegel, A.C., Tang, S.K.Y., Nijhuis, C.A., Hashimoto, M., Phillips, S.T., Dickey, M.D. and Whitesides, G.M., Cofabrication: a strategy for building multicomponent Microsystems. Accounts of Chemical Research, 2010, 43: 518–528.CrossRefGoogle Scholar
  45. [45]
    Jones, J., Lacour, S.P., Wagner, S. and Suo, Z., Stretchable wavy metal interconnects. Journal of Vacuum Science & Technology A, 2004, 22: 1723–1725.CrossRefGoogle Scholar
  46. [46]
    Brosteaux, D., Axisa, F., Gonzalez, M. and Vanfleteren, J., Design and fabrication of elastic interconnections for stretchable electronic circuits. IEEE Electron Device Letters, 2007, 28: 552–554.CrossRefGoogle Scholar
  47. [47]
    Zoumpoulidisa, T., Barteka, M., de Graafb, P. and Dekkera, R., High-aspect-ratio through-wafer parylene beams for stretchable silicon electronics. Sensors and Actuators A: Physical, 2009, 156: 257–264.CrossRefGoogle Scholar
  48. [48]
    Hsu, Y.Y., Gonzalez, M., Wolf, I.D., In situ observations on deformation behavior and stretchinginduced failure of fine pitch stretchable interconnect. Journal of Materials Research, 2009, 24: 3573–3582.CrossRefGoogle Scholar
  49. [49]
    Kim, H.J., Maleki, T., Wei, P., Ziaie, B. and Member, S., A biaxial stretchable interconnect with liquid-alloy-covered joints on elastomeric substrate. Journal of Microelectromechanical systems, 2009, 18: 138–146.CrossRefGoogle Scholar
  50. [50]
    Lin, K.L. and Jain, K., Design and fabrication of stretchable multilayer self-aligned interconnects for flexible electronics and large-area sensor arrays using excimer laser photoablation. IEEE Electron Device Letters, 2009, 30: 14–17.CrossRefGoogle Scholar
  51. [51]
    Huang, Y., Zhou, W., Hsia, K.J., Menard, E., Park, J.U., Rogers, J.A. and Alleyne, A.G., Stamp collapse in soft lithography. Langmuir, 2005, 21: 8058–8068.CrossRefGoogle Scholar
  52. [52]
    Hsia, K.J., Huang, Y., Menard, E., Park, J.U., Zhou, W., Rogers, J.A. and Fulton, J.M., Collapse of stamps for soft lithography due to interfacial adhesion. Applied Physics Letters, 2005, 86: 154106.CrossRefGoogle Scholar
  53. [53]
    Zhou, W., Huang, Y., Menard, E., Aluru, N.R., Rogers, J.A. and Alleyne, A.G., Mechanism for stamp collapse in soft lithography. Applied Physics Letters, 2005, 87: 251925.CrossRefGoogle Scholar
  54. [54]
    Meitl, M.A., Zhu, Z.T., Kumar, V., Lee, K.J., Feng, X., Huang, Y., Adesida, I., Nuzzo, R.G. and Rogers, J.A., Transfer printing by kinetic control of adhesion to an elastomeric stamp. Nature Materials, 2006, 5: 33–38.CrossRefGoogle Scholar
  55. [55]
    Meitl, M.A., Feng, X., Dong, J., Menard, E., Ferreira, P., Huang, Y. and Rogers, J.A., Stress focusing for controlled fracture in microelectromechanical systems. Applied Physics Letters, 2007, 90: 083110.CrossRefGoogle Scholar
  56. [56]
    Feng, X., Meitl, M.A., Bowen, A.M., Huang, Y., Nuzzo, R.G. and Rogers, J.A., Competing fracture in kinetically controlled transfer printing. Langmuir, 2007, 23: 12555–12560.CrossRefGoogle Scholar
  57. [57]
    Kim, T.H., Carlson, A., Ahn, J.H., Won, S.M., Wang, S., Huang, Y. and Rogers, J.A., Kinetically controlled, adhesiveless transfer printing using microstructured stamps. Applied Physics Letters, 2009, 94: 113502.CrossRefGoogle Scholar
  58. [58]
    Kim, S., Wu, J., Carlson, A., Jin, S.H., Kovalsky, A., Glass, P., Liu, Z., Ahmed, N., Elgan, S.L., Chen, W., Ferreira, P.M., Sitti, M., Huang, Y. and Rogers, J.A., Microstructured elastomeric surfaces with reversible adhesion and examples of their use in deterministic assembly by transfer printing. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107: 17095–17100.CrossRefGoogle Scholar
  59. [59]
    Kim, D.H., Kim, Y.S., Wu, J., Liu, Z., Song, J., Kim, H.S., Huang, Y., Hwang K.C. and Rogers, J.A., Ultrathin silicon circuits with strain-isolation layers and mesh layouts for high-performance electronics on fabric, vinyl, leather, and paper. Advanced Materials, 2009, 21: 3703–3707.CrossRefGoogle Scholar
  60. [60]
    Kim, D.H., Song, J., Choi, W.M., Kim, H.S., Kim, R.H., Liu, Z., Huang, Y., Hwang, K.C., Zhang, Y.W. and Rogers, J.A., Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations. Proceedings of the National Academy of Sciences of the United States of America, 2008, 105: 18675–18680.CrossRefGoogle Scholar
  61. [61]
    Song, J., Huang, Y., Xiao, J., Wang, S., Hwang, K.C., Ko, H.C., Kim, D.H., Stoykovich, M.P. and Rogers, J.A., Mechanics of non-coplanar mesh design for stretchable electronic circuits. Journal of Applied Physics, 2009, 105: 123516.CrossRefGoogle Scholar
  62. [62]
    Bowden, N., Brittain, S., Evans, A.G., Hutchinson, J.W. and Whitesides, G.M., Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature, 1998, 393: 146–149.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  • Ming Li
    • 1
    • 2
  • Jianliang Xiao
    • 3
  • Jian Wu
    • 2
  • Rak-Hwan Kim
    • 3
  • Zhan Kang
    • 1
  • Yonggang Huang
    • 2
  • John A. Rogers
    • 3
  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  2. 2.Departments of Civil and Environmental Engineering and Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Department of Materials Science and Engineering, Beckman Institute for Advanced Science and Technology, and Frederick Seitz Materials Research LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations