Acta Mechanica Solida Sinica

, Volume 31, Issue 5, pp 573–588 | Cite as

Robustly Tuning Bandgaps in Two-Dimensional Soft Phononic Crystals with Criss-Crossed Elliptical Holes

  • Nan Gao
  • Yi-lan Huang
  • Rong-hao BaoEmail author
  • Wei-qiu ChenEmail author


Tuning band gaps in soft materials by post-buckling deformation is becoming an appealing means to manipulate elastic waves. As one of the most favorable topologies, two-dimensional soft structures with circular holes have been extensively studied. Based on the contrarian thinking, this paper starts from the two-dimensional soft structures with criss-crossed elliptical holes, which is close to the post-buckling configuration of soft structures with circular holes, and then proposes to tune the band gaps through elongating or stretching rather than compressing. Influences of the loading magnitude and loading pattern (i.e., uniaxial and biaxial elongations) on the band gaps are studied via the nonlinear finite element simulations. Effects of the geometric parameters (the major-to-minor half-axis ratio and the porosity of the structure) are also discussed. It is shown that, compared with the traditional circular hole case, the band gaps of the unloaded structure with criss-crossed elliptical holes are much richer, and they could be reversely and continuously tuned by tensile loadings. In particular, the deformation is very robust and is insensitive to small geometric imperfections, which is always necessary for triggering the post-buckling deformations. The present work provides a useful reference to the manipulation of elastic waves in periodic structures as well as the design of soft phononic crystals/acoustic devices.


Soft phononic crystal Criss-crossed elliptical holes Band gap Tunability 



The work was supported by the National Natural Science Foundation of China (11532001, 11621062). Partial support from the Fundamental Research Funds for the Central Universities (No. 2016XZZX001-05) is also acknowledged. The work was also supported by the Shenzhen Scientific and Technological Fund for R & D (No. JCYJ20170816172316775).


  1. 1.
    Sigalas MM, Economou EN. Elastic and acoustic wave band structure. J Sound Vib. 1992;158:377–82.CrossRefGoogle Scholar
  2. 2.
    Kushwaha MS, Halevi P, Martinez G. Theory of acoustic band structure of periodic elastic composites. Phys Rev B. 1994;49:2313.CrossRefGoogle Scholar
  3. 3.
    Bertoldi K, Boyce MC. Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Phys Rev B. 2008;77:052105.CrossRefGoogle Scholar
  4. 4.
    Bertoldi K, Boyce MC. Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations. Phys Rev B. 2008;78:184107.CrossRefGoogle Scholar
  5. 5.
    Huang Y, Shen X, Zhang C. Mechanically tunable band gaps in compressible soft phononic laminated composites with finite deformation. Phys Lett A. 2014;378:2285–9.CrossRefGoogle Scholar
  6. 6.
    Rudykh S, Boyce MC. Transforming wave propagation in layered media via instability-induced interfacial wrinkling. Phys Rev Lett. 2014;112:034301.CrossRefGoogle Scholar
  7. 7.
    Bertoldi K, Boyce MC, Deschanel S. Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures. J Mech Phys Solids. 2008;56:2642–68.CrossRefGoogle Scholar
  8. 8.
    Wang P, Casadei F, Kang SH. Locally resonant band gaps in periodic beam lattices by tuning connectivity. Phys Rev B. 2015;91:020103.CrossRefGoogle Scholar
  9. 9.
    Qi JL, Wang P, Koh SJA. Wave propagation in fractal-inspired self-similar beam lattices. Appl Phys Lett. 2015;107:221911.CrossRefGoogle Scholar
  10. 10.
    Huang Y, Gao N, Chen W. Extension/compression-controlled complete band gaps in 2D chiral square-lattice-like structures. Acta Mech Solida Sin. 2018;31:1–15.CrossRefGoogle Scholar
  11. 11.
    Dowling JP. Sonic band structure in fluids with periodic density variations. J Acoust Soc Am. 1992;91:2539–43.CrossRefGoogle Scholar
  12. 12.
    Sigalas M, Soukoulis C. Elastic-wave propagation through disordered and/or absorptive layered systems. Phys Rev B. 1995;51:2780.CrossRefGoogle Scholar
  13. 13.
    Ao X, Chan CT. Complex band structures and effective medium descriptions of periodic acoustic composite systems. Phys Rev B. 2009;80:235118.CrossRefGoogle Scholar
  14. 14.
    Liu Z, Chan CT, Sheng P. Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys Rev B. 2000;62:2446.CrossRefGoogle Scholar
  15. 15.
    Garcia-Pablos D, Sigalas M, De Espinosa FM. Theory and experiments on elastic band gaps. Phys Rev Lett. 2000;84:4349.CrossRefGoogle Scholar
  16. 16.
    Sigalas M, Garcıa N. Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method. J Appl Phys. 2000;87:3122–5.CrossRefGoogle Scholar
  17. 17.
    Mead DJ. A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. J Sound Vib. 1973;27:235–60.CrossRefGoogle Scholar
  18. 18.
    Philippe L, Hladky-Hennion A-C, Decarpigny J-N. Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method. J Acoust Soc Am. 1995;98:2792–800.CrossRefGoogle Scholar
  19. 19.
    Gao N, Li J, Bao R, et al. Study of the band gaps of two dimensional phononic crystals with criss-crossed elliptical holes. J Zhejiang Univ (Eng Sci). 2018 (in Chinese) (accepted).Google Scholar
  20. 20.
    Abaqus 6.14. Abaqus analysis user’s guide. Vélizy-Villacoublay: Dassault Systèmes Simulia Corporation; 2014.Google Scholar
  21. 21.
    Åberg M, Gudmundson P. The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure. J Acoust Soc Am. 1997;102:2007–13.CrossRefGoogle Scholar
  22. 22.
    Safavi-Naeini AH, Painter O. Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic–photonic crystal slab. Opt Express. 2010;18:14926–43.CrossRefGoogle Scholar
  23. 23.
    Javid F, Wang P, Shanian A, Bertoldi K. Architected materials with ultra-low porosity for vibration control. Adv Mater. 2016;28:5943–8.CrossRefGoogle Scholar
  24. 24.
    Dong HW, Su XX, Wang YS. Multi-objective optimization of two-dimensional porous phononic crystals. J Phys D Appl Phys. 2014;47:155301.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018
corrected publication August 2018

Authors and Affiliations

  1. 1.Department of Engineering MechanicsZhejiang UniversityHangzhouChina
  2. 2.State Key Lab of CAD & CGZhejiang UniversityHangzhouChina
  3. 3.Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhouChina
  4. 4.Soft Matter Research CenterZhejiang UniversityHangzhouChina

Personalised recommendations