Research Papers

Generalized Method to Analyze Acoustomechanical Stability of Soft Materials

[+] Author and Article Information
Fengxian Xin

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an 710049, China;
MOE Key Laboratory for Multifunctional
Materials and Structures,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: fengxian.xin@gmail.com

Tianjian Lu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an 710049, China;
MOE Key Laboratory for Multifunctional
Materials and Structures,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tjlu@mail.xjtu.edu.cn

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 1, 2016; final manuscript received April 11, 2016; published online May 5, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(7), 071004 (May 05, 2016) (4 pages) Paper No: JAM-16-1066; doi: 10.1115/1.4033429 History: Received February 01, 2016; Revised April 11, 2016

Acoustic radiation force generated by two counterpropagating acoustic waves in a thin layer of soft material can induce large deformation, and hence can be applied to design acoustomechanical actuators. Owing to the sensitivity of wave propagation to material geometry, the change of layer thickness may enhance wave propagation and acoustic radiation force, causing a jumping larger deformation, i.e., snap-through instability. Built upon the basis of strong elliptic condition, we develop a generalized theoretical method to evaluate the acoustomechanical stability of soft material actuators. We demonstrate that acoustomechanical instability occurs when the true tangential stiffness matrix ceases to be positive definite. Our results show that prestresses can not only enhance significantly the acoustomechanical stability of the soft material layer but also amplify its actuation stretch in thickness direction.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Pelrine, R. , Kornbluh, R. , Pei, Q. , and Joseph, J. , 2000, “ High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287(5454), pp. 836–839. [CrossRef] [PubMed]
Zhang, Q. M. , Li, H. , Poh, M. , Xia, F. , Cheng, Z. Y. , Xu, H. , and Huang, C. , 2002, “ An All-Organic Composite Actuator Material With a High Dielectric Constant,” Nature, 419(6904), pp. 284–287. [CrossRef] [PubMed]
Plante, J.-S. , and Dubowsky, S. , 2006, “ Large-Scale Failure Modes of Dielectric Elastomer Actuators,” Int. J. Solids Struct., 43(25–26), pp. 7727–7751. [CrossRef]
Ha, S. M. , Yuan, W. , Pei, Q. , Pelrine, R. , and Stanford, S. , 2006, “ Interpenetrating Polymer Networks for High-Performance Electroelastomer Artificial Muscles,” Adv. Mater., 18(7), pp. 887–891. [CrossRef]
Patrick, L. , Gabor, K. , and Silvain, M. , 2007, “ Characterization of Dielectric Elastomer Actuators Based on a Hyperelastic Film Model,” Sens. Actuators, A, 135(2), pp. 748–757. [CrossRef]
Goulbourne, N. C. , Mockensturm, E. M. , and Frecker, M. I. , 2007, “ Electro-Elastomers: Large Deformation Analysis of Silicone Membranes,” Int. J. Solids Struct., 44(9), pp. 2609–2626. [CrossRef]
Plante, J. S. , and Dubowsky, S. , 2007, “ On the Properties of Dielectric Elastomer Actuators and Their Design Implications,” Smart Mater. Struct., 16(2), pp. S227–S236. [CrossRef]
Hong, W. , Zhao, X. , Zhou, J. , and Suo, Z. , 2008, “ A Theory of Coupled Diffusion and Large Deformation in Polymeric Gels,” J. Mech. Phys. Solids, 56(5), pp. 1779–1793. [CrossRef]
Suo, Z. , 2010, “ Theory of Dielectric Elastomers,” Acta Mech. Solida Sin., 23(6), pp. 549–578. [CrossRef]
Zhao, X. , and Wang, Q. , 2014, “ Harnessing Large Deformation and Instabilities of Soft Dielectrics: Theory, Experiment, and Application,” Appl. Phys. Rev., 1(2), p. 021304. [CrossRef]
Hong, W. , Zhao, X. , and Suo, Z. , 2010, “ Large Deformation and Electrochemistry of Polyelectrolyte Gels,” J. Mech. Phys. Solids, 58(4), pp. 558–577. [CrossRef]
Xiaoyi Chen, H.-H. D. , 2015, “ Swelling and Instability of a Gel Annulus,” Acta Mech. Sin., 31(5), pp. 627–636. [CrossRef]
Stark, K. H. , and Garton, C. G. , 1955, “ Electric Strength of Irradiated Polythene,” Nature, 176(4495), pp. 1225–1226. [CrossRef]
Zhao, X. , and Suo, Z. , 2007, “ Method to Analyze Electromechanical Stability of Dielectric Elastomers,” Appl. Phys. Lett., 91(6), p. 061921. [CrossRef]
Díaz-Calleja, R. , Riande, E. , and Sanchis, M. J. , 2008, “ On Electromechanical Stability of Dielectric Elastomers,” Appl. Phys. Lett., 93(10), p. 101902. [CrossRef]
Zhao, X. , Hong, W. , and Suo, Z. , 2007, “ Electromechanical Hysteresis and Coexistent States in Dielectric Elastomers,” Phys. Rev. B, 76(13), p. 134113. [CrossRef]
Xin, F. X. , and Lu, T. J. , “ Acoustomechanical Constitutive Theory of Soft Materials,” Acta Mech. Sin. (in press).
Xin, F. , and Lu, T. , 2016, “ Acoustomechanics of Semicrystalline Polymers,” Theor. Appl. Mech. Lett., 6(1), pp. 38–41. [CrossRef]
Karki, B. B. , Ackland, G. J. , Crain, J. , Karki, B. B. , Ackland, G. J. , and Crain, J. , 1997, “ Elastic Instabilities in Crystals From Ab Initio Stress–Strain Relations,” J. Phys.: Condens. Matter, 9(41), pp. 8579–8589. [CrossRef]
Li, W. , and Wang, T. , 1999, “ Elasticity, Stability, and Ideal Strength of β-SiC in Plane-Wave-Based Ab Initio Calculations,” Phys. Rev. B, 59(6), pp. 3993–4001. [CrossRef]
Wang, J. , Li, J. , Yip, S. , Phillpot, S. , and Wolf, D. , 1995, “ Mechanical Instabilities of Homogeneous Crystals,” Phys. Rev. B, 52(17), pp. 12627–12635. [CrossRef]
Gent, A. N. , 1996, “ A New Constitutive Relation for Rubber,” Rubber Chem. Technol., 69(1), pp. 59–61. [CrossRef]
Lee, C. P. , and Wang, T. G. , 1993, “ Acoustic Radiation Pressure,” J. Acoust. Soc. Am., 94(2), pp. 1099–1109. [CrossRef]
Silva, G. T. , Chen, S. , Greenleaf, J. F. , and Fatemi, M. , 2005, “ Dynamic Ultrasound Radiation Force in Fluids,” Phys. Rev. E, 71(5), p. 056617. [CrossRef]


Grahic Jump Location
Fig. 2

Acoustomechanical response of soft material actuator to different levels of equal-biaxial mechanical prestresses: (a) normalized acoustic force versus in-plane stretch λ1 and (b) normalized acoustic force versus normalized in-plane stretch λ1/λ1p. Critical onsets of acoustomechanical instabilities are marked by crosses.

Grahic Jump Location
Fig. 1

(a) Acoustomechanical deformation of a soft material layer subject to combined biaxial stresses and acoustic inputs and (b) biaxial stresses and equivalent acoustic forces

Grahic Jump Location
Fig. 3

Effect of unequal biaxial mechanical prestresses on (a) critical acoustic force pc, (b) critical in-plane actuation stretch λ1c, (c) critical in-plane actuation stretch λ2c, and (d) critical out-of-plane actuation stretch λ3c



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