Research Papers

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

[+] Author and Article Information
Pu Zhang

School of Mathematics,
University of Manchester,
Oxford Road,
Manchester M13 9PL, UK
e-mail: puz1@pitt.edu

William J. Parnell

School of Mathematics,
University of Manchester,
Oxford Road,
Manchester M13 9PL, UK
e-mail: William.Parnell@manchester.ac.uk

Manuscript received May 18, 2017; final manuscript received July 17, 2017; published online July 26, 2017. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 84(9), 091007 (Jul 26, 2017) (7 pages) Paper No: JAM-17-1263; doi: 10.1115/1.4037314 History: Received May 18, 2017; Revised July 17, 2017

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of “bands-sticking-together” is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying prestretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Hussein, M. I. , Leamy, M. J. , and Ruzzene, M. , 2014, “ Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook,” ASME Appl. Mech. Rev., 66(4), p. 040802. [CrossRef]
Laude, V. , 2015, Phononic Crystals: Artificial Crystals for Sonic, Acoustic, and Elastic Waves, Vol. 26, Walter de Gruyter GmbH, Berlin. [CrossRef]
Zhang, P. , and To, A. C. , 2013, “ Broadband Wave Filtering of Bioinspired Hierarchical Phononic Crystal,” Appl. Phys. Lett., 102(12), p. 121910. [CrossRef]
Barnwell, E. G. , Parnell, W. J. , and David Abrahams, I. , 2017, “ Tunable Elastodynamic Band Gaps,” Extreme Mech. Lett., 12, pp. 23–29. [CrossRef]
Bertoldi, K. , and Boyce, M. C. , 2008, “ Wave Propagation and Instabilities in Monolithic and Periodically Structured Elastomeric Materials Undergoing Large Deformations,” Phys. Rev. B, 78(18), p. 184107. [CrossRef]
Galich, P. I. , Fang, N. X. , Boyce, M. C. , and Rudykh, S. , 2017, “ Elastic Wave Propagation in Finitely Deformed Layered Materials,” J. Mech. Phys. Solids, 98, pp. 390–410. [CrossRef]
Robillard, J.-F. , Bou Matar, O. , Vasseur, J. O. , Deymier, P. A. , Stippinger, M. , Hladky-Hennion, A.-C. , Pennec, Y. , and Djafari-Rouhani, B. , 2009, “ Tunable Magnetoelastic Phononic Crystals,” Appl. Phys. Lett., 95(12), p. 124104. [CrossRef]
Shmuel, G. , 2013, “ Electrostatically Tunable Band Gaps in Finitely Extensible Dielectric Elastomer Fiber Composites,” Int. J. Solids Struct., 50(5), pp. 680–686. [CrossRef]
Zhang, P. , and Parnell, W. J. , 2017, “ Soft Phononic Crystals With Deformation-Independent Band Gaps,” Proc. R. Soc. A, 473(2200), p. 20160865. [CrossRef]
Ma, G. , and Sheng, P. , 2016, “ Acoustic Metamaterials: From Local Resonances to Broad Horizons,” Sci. Adv., 2(2), p. e1501595. [CrossRef] [PubMed]
Babaee, S. , Viard, N. , Wang, P. , Fang, N. X. , and Bertoldi, K. , 2016, “ Harnessing Deformation to Switch On and Off the Propagation of Sound,” Adv. Mater., 28(8), pp. 1631–1635. [CrossRef] [PubMed]
Lu, N. , and Kim, D.-H. , 2014, “ Flexible and Stretchable Electronics Paving the Way for Soft Robotics,” Soft Rob., 1(1), pp. 53–62. [CrossRef]
Lv, C. , Yu, H. , and Jiang, H. , 2014, “ Archimedean Spiral Design for Extremely Stretchable Interconnects,” Extreme Mech. Lett., 1, pp. 29–34. [CrossRef]
Rogers, J. A. , Someya, T. , and Huang, Y. , 2010, “ Materials and Mechanics for Stretchable Electronics,” Science, 327(5973), pp. 1603–1607. [CrossRef] [PubMed]
Zhang, Y. , Fu, H. , Su, Y. , Xu, S. , Cheng, H. , Fan, J. A. , Hwang, K.-C. , Rogers, J. A. , and Huang, Y. , 2013, “ Mechanics of Ultra-Stretchable Self-Similar Serpentine Interconnects,” Acta Mater., 61(20), pp. 7816–7827. [CrossRef]
Trainiti, G. , Rimoli, J. J. , and Ruzzene, M. , 2015, “ Wave Propagation in Periodically Undulated Beams and Plates,” Int. J. Solids Struct., 75–76, pp. 260–276. [CrossRef]
Becker, L. E. , Chassie, G. G. , and Cleghorn, W. L. , 2002, “ On the Natural Frequencies of Helical Compression Springs,” Int. J. Mech. Sci., 44(4), pp. 825–841. [CrossRef]
Pearson, D. , 1982, “ The Transfer Matrix Method for the Vibration of Compressed Helical Springs,” J. Mech. Eng. Sci., 24(4), pp. 163–171. [CrossRef]
Frikha, A. , Treyssede, F. , and Cartraud, P. , 2011, “ Effect of Axial Load on the Propagation of Elastic Waves in Helical Beams,” Wave Motion, 48(1), pp. 83–92. [CrossRef]
Audoly, B. , and Pomeau, Y. , 2010, Elasticity and Geometry: From Hair Curls to the Non-Linear Response of Shells, Oxford University Press, Oxford, UK.
Neukirch, S. , Frelat, J. , Goriely, A. , and Maurini, C. , 2012, “ Vibrations of Post-Buckled Rods: The Singular Inextensible Limit,” J. Sound Vib., 331(3), pp. 704–720. [CrossRef]
Ogden, R. W. , 2007, “ Incremental Statics and Dynamics of Pre-Stressed Elastic Materials,” Waves in Nonlinear Pre-Stressed Materials, Springer, New York, pp. 1–26. [CrossRef]
Bellman, R. , 1997, Introduction to Matrix Analysis, SIAM, Philadelphia, PA.
Maurin, F. , and Spadoni, A. , 2014, “ Wave Dispersion in Periodic Post-Buckled Structures,” J. Sound Vib., 333(19), pp. 4562–4578. [CrossRef]
Trainiti, G. , Rimoli, J. J. , and Ruzzene, M. , 2016, “ Wave Propagation in Undulated Structural Lattices,” Int. J. Solids Struct., 97–98, pp. 431–444. [CrossRef]
Chen, Y. , Li, T. , Scarpa, F. , and Wang, L. , 2017, “ Lattice Metamaterials With Mechanically Tunable Poissons Ratio for Vibration Control,” Phys. Rev. Appl., 7(2), p. 024012. [CrossRef]
Dresselhaus, M. S. , Dresselhaus, G. , and Jorio, A. , 2007, Group Theory: Application to the Physics of Condensed Matter, Springer Science & Business Media, Berlin.
Mock, A. , Lu, L. , and O'Brien, J. , 2010, “ Space Group Theory and Fourier Space Analysis of Two-Dimensional Photonic Crystal Waveguides,” Phys. Rev. B, 81(15), p. 155115. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic illustration of two forms of stretchable serpentine interconnects. The relaxed configurations are described by Eqs. (1) and (2).

Grahic Jump Location
Fig. 2

Schematic illustration of the relaxed and stretched configurations of the serpentine interconnects.

Grahic Jump Location
Fig. 3

Comparison of the dispersion curves obtained from the current elastica model and the undulated beam model [16]. The geometric parameters are chosen as H0/L0=0.05,β=0, and the thickness of the beam is 0.07L0.

Grahic Jump Location
Fig. 4

Phononic band structures of serpentine interconnects in the relaxed state. The dispersion curves are indicated by dotted curves, while the band gaps are represented by shaded areas. (a) H0/L0=2, β=0, (b) H0/L0=1, β=0, (c) H0/L0=0.5, β=0, (d) H0/L0=2, β=0.2, (e) H0/L0=1, β=0.2, and (f) H0/L0=0.5, β=0.2.

Grahic Jump Location
Fig. 5

Phononic band structures of prestretched serpentine interconnects with β = 0: (a) Λ = 2, (b) Λ = 5, (c) Λ = 7, and (d) band gaps for different stretch ratio Λ

Grahic Jump Location
Fig. 6

Phononic band structures of prestretched serpentine interconnects with β=0.2: (a) Λ = 3, (b) Λ = 5, (c) Λ = 8, and (d) band gaps for different stretch ratio Λ

Grahic Jump Location
Fig. 7

Bloch wave modes for relaxed ((a) and (c)) and prestretched ((b) and (d)) serpentine interconnects. The stationary configurations are indicated by dashed–doted curves, while the Bloch wave modes are represented by solid curves. The wave number is chosen as k¯=π/2, and the eigenfrequencies ω¯1 and ω¯2 indicate the first and second bands, respectively. The geometric parameters are chosen as H0/L0=2 and β = 0 for all cases: (a) ω¯1  = 8.73, Λ = 1, (b) ω¯1  = 8.92, Λ = 2, (c) ω¯2  = 9.79, Λ = 1, and (d) ω¯2  = 10.28, Λ = 2.

Grahic Jump Location
Fig. 8

Phononic band structures of prestretched serpentine interconnects when internal forces are neglected. The aspect ratio is H0/L0=2 for all cases. (a) β=0, Λ=2; (b) β=0, Λ=7; (c) β=0.2, Λ=3; (d) β=0.2, Λ=8.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In