0
Research Papers

Electromechanical Modeling of Softening Behavior for Dielectric Elastomers

[+] Author and Article Information
Xiongfei Lv

Department of Astronautic Science
and Mechanics,
Harbin Institute of
Technology (HIT),
No. 92 West Dazhi Street,
P.O. Box 301,
Harbin 150001, China

Liwu Liu

Department of Astronautic Science and
Mechanics,
Harbin Institute of Technology (HIT),
No. 92 West Dazhi Street
P.O. Box 301,
Harbin 150001, China

Yanju Liu

Department of Astronautic Science and
Mechanics,
Harbin Institute of Technology (HIT),
No. 92 West Dazhi Street,
P.O. Box 301,
Harbin 150001, China
e-mail: yj_liu@hit.edu.cn

Jinsong Leng

Centre for Composite Materials and Structures,
Harbin Institute of Technology (HIT),
No. 2 Yikuang Street,
P.O. Box 3011,
Harbin 150080, China

1X. Lv and L. Liu contributed equally to this work.

2Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 30, 2018; final manuscript received May 20, 2018; published online August 31, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 85(11), 111010 (Aug 31, 2018) (10 pages) Paper No: JAM-18-1063; doi: 10.1115/1.4040405 History: Received January 30, 2018; Revised May 20, 2018

Dielectric elastomer (DE) is a promising electroactive polymer. As DE material, rubbers are often filled with functional particles to improve their electromechanical performance. However, the filled particles also bring stress softening, which is known as Mullins effect. In this paper, we prepared the carbon nanotube filled silicone elastomer (SE) as DE composite and modeled its Mullins effect using the pseudo-elastic theory. Then, the thermodynamics of DE was combined to predict the idealized electromechanical softening behavior. Two cases are considered: linear dielectric and saturated dielectric. For linear dielectric with an initial force, “residual strain” will appear after every voltage-controlled cycle, and instability may be eliminated in reloading. For saturated dielectric, the material response changes a lot after saturation, which also affects the subsequent softening behavior. At last, viscoelasticity was further incorporated to account for rate-dependent softening deformation, and we also carried out some simple electromechanical experiments on VHB 4910 to explore its softening behavior. This work may lead to a better understanding of the softening behavior in DEs undergoing electromechanical coupling situations.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Pelrine, R. , Kornbluh, R. , Pei, Q. B. , and Joseph, J. , 2000, “ High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287(5454), pp. 836–839. [CrossRef] [PubMed]
Carpi, F. , Bauer, S. , and DeRossi, D. , 2010, “ Stretching Dielectric Elastomer Performance,” Science, 330(6012), pp. 1759–1761. [CrossRef] [PubMed]
Brochu, P. , and Pei, Q. B. , 2010, “ Advances in Dielectric Elastomers for Actuators and Artificial Muscles,” Macromol. Rapid Commun., 31(1), pp. 10–36. [CrossRef] [PubMed]
Bar-Cohen, Y. , 2000, “ Electroactive Polymers as Artificial Muscles Capabilities, Potentials and Challenges,” Handbook on Biomimetics, Y. Osada , ed., NTS Inc., Bakersfield, CA, pp. 1–13.
Bar-Cohen, Y. , 2006, “ Biologically Inspired Technology Using Electroactive Polymers (EAP),” Proc. SPIE, 6168, p. 616803.
Liu, Y. J. , Liu, L. W. , Zhang, Z. , Jiao, Y. , Sun, S. H. , and Leng, J. S. , 2010, “ Analysis and Manufacture of an Energy Harvester Based on a Mooney-Rivlin-Type Dielectric Elastomer,” Europhys. Lett., 90(3), p. 36004. [CrossRef]
Lv, X. F. , Liu, L. W. , Liu, Y. J. , and Leng, J. S. , 2015, “ Dielectric Elastomer Energy Harvesting: Maximal Converted Energy, Viscoelastic Dissipation and a Wave Power Generator,” Smart Mater. Struct., 24(11), p. 115036. [CrossRef]
Liu, L. W. , Liu, Y. J. , Zhang, Z. , Li, B. , and Leng, J. S. , 2010, “ Electromechanical Stability of Electro-Active Silicone Filled With High Permittivity Particles Undergoing Large Deformation,” Smart Mater. Struct., 19(11), p. 115025. [CrossRef]
Liu, L. W. , Zhang, Z. , Li, J. R. , Li, T. F. , Liu, Y. J. , and Leng, J. S. , 2015, “ Stability of Dielectric Elastomer/Carbon Nanotube Composites Coupling Electrostriction and Polarization,” Compos. Part B: Eng., 78, pp. 35–41. [CrossRef]
Bueche, F. , 1960, “ Molecular Basis for the Mullins Effect,” J. Appl. Polym. Sci., 4(10), pp. 107–114. [CrossRef]
Bueche, F. , 1961, “ Mullins Effect and Rubber–Filler Interaction,” J. Appl. Polym. Sci., 5(15), pp. 271–281. [CrossRef]
Mullins, L. , 1948, “ Effect of Stretching on the Properties of Rubber,” Rubber Chem. Technol., 21(2), pp. 281–300.
Mullins, L. , 1969, “ Softening of Rubber by Deformation,” Rubber Chem. Technol., 42(1), pp. 339–362. [CrossRef]
Lu, T. Q. , Wang, J. K. , Yang, R. S. , and Wang, T. J. , 2017, “ A Constitutive Model for Soft Materials Incorporating Viscoelasticity and Mullins Effect,” ASME J. Appl. Mech., 84(2), p. 021010. [CrossRef]
Mullins, L. , and Tobin, N. R. , 1957, “ Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers,” Rubber Chem. Technol., 30(2), pp. 555–571. [CrossRef]
Ogden, R. W. , and Roxburgh, D. G. , 1999, “ A Pseudo-Elastic Model for the Mullins Effect in Filled Rubber,” Proc. R. Soc. London A, 455(1988), pp. 2861–2877. [CrossRef]
Dorfmann, A. , and Ogden, R. W. , 2003, “ A Pseudo-Elastic Model for Loading, Partial Unloading and Reloading of Particle-Reinforced Rubber,” Int. J. Solids Struct., 40(11), pp. 2699–2714. [CrossRef]
Dorfmann, A. , and Ogden, R. W. , 2004, “ A Constitutive Model for the Mullins Effect With Residual Strain in Particle Reinforced Rubber,” Int. J. Solids Struct., 41(7), pp. 1855–1878. [CrossRef]
Yeom, K. S. , Jeong, S. , Huh, H. , and Park, J. , 2013, “ New Pseudo-Elastic Model for Polymer-Bonded Explosive Simulants Considering the Mullins Effect,” J. Compos. Mater., 47(27), pp. 3401–3412. [CrossRef]
Rickaby, S. R. , and Scott, N. H. , 2013, “ A Model for the Mullins Effect During Multicyclic Equibiaxial Loading,” Acta Mech., 224(9), pp. 1887–1900. [CrossRef]
Rickaby, S. R. , and Scott, N. H. , 2013, “ Cyclic Stress-Softening Model for the Mullins Effect in Compression,” Int. J. Nonlinear Mech., 49, pp. 152–158. [CrossRef]
Rickaby, S. R. , and Scott, N. H. , 2013, “ A Cyclic Stress Softening Model for the Mullins Effect,” Int. J. Solids Struct., 50(1), pp. 111–120. [CrossRef]
Chagnon, G. , Verron, E. , Gorne, T. L. , Marckmann, G. , and Charrier, P. , 2004, “ On the Relevance of Continuum Damage Mechanics as Applied to the Mullins Effect in Elastomers,” J. Mech. Phys. Solids, 52(7), pp. 1627–1650. [CrossRef]
Loo, M. S. , Andriyana, A. , Lee, S. L. , and Tan, N. H. , 2014, “ A Continuum Mechanical Modelling of Mullins Effect in Swollen Elastomers,” Mater. Res. Innov., 18(Suppl. 6), pp. 56–60.
Rivlin, R. S. , 1948, “ Large Elastic Deformations of Isotropic Materials. II, Some Uniqueness Theorems for Pure Homogeneous Deformations,” Philos. Trans. Roy. Soc. A, 240(822), pp. 419–508.
Rivlin, R. S. , 1951, “ Large Elastic Deformations of Isotropic Materials. VII, Experiments on the Deformation of Rubber,” Philos. Trans. Roy. Soc. A, 243(865), pp. 251–288. [CrossRef]
Mooney, M. , 1940, “ A Theory of Large Elastic Deformation,” J. Appl. Phys., 11(9), pp. 582–592. [CrossRef]
Yeoh, O. H. , 1990, “ Characterization of Elastic Properties of Carbon Black-Filled Rubber Vulcanizates,” Rubber. Chem. Technol., 63(5), pp. 792–805.
Suo, Z. G. , 2010, “ Theory of Dielectric Elastomers,” Acta Mech. Solida Sin., 23(6), pp. 549–578. [CrossRef]
Liu, L. W. , Liu, Y. J. , Luo, X. J. , Li, B. , and Leng, J. S. , 2012, “ Electromechanical Instability and Snap-Through Instability of Dielectric Elastomers Undergoing Polarization Saturation,” Mech. Mater., 55, pp. 60–72. [CrossRef]
Hong, W. , 2011, “ Modeling Viscoelastic Dielectrics,” J. Mech. Phys. Solids., 59(3), pp. 637–650. [CrossRef]
Foo, C. C. , Cai, S. Q. , Koh, S. J. A. , Bauer, S. , and Suo, Z. G. , 2012, “ Model of Dissipative Dielectric Elastomers,” J. Appl. Phys., 111(3), p. 034102. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Molecular chains and particles before, during, and after loading

Grahic Jump Location
Fig. 2

Stress–stretch relation of idealized Mullins effect

Grahic Jump Location
Fig. 3

Preparation process of CNT filled silicon elastomer

Grahic Jump Location
Fig. 4

Relative permittivity and dielectric loss of silicone composite with different CNTs content at varying frequencies [9] (Reprinted with permission from Elsevier © 2015)

Grahic Jump Location
Fig. 5

Step-up (a) and step-down (b) curves for 3% CNT/SE and step-up curves for 5% CNT/SE

Grahic Jump Location
Fig. 6

Fitting results with different models (a) and of Mullins effect (b)

Grahic Jump Location
Fig. 7

Nominal electric field—stretch curves with different initial forces (a) and nominal stress–stretch curves with different initial voltages (b)

Grahic Jump Location
Fig. 8

Idealized voltage-controlled loading and unloading curves with s/C10=0 (a) and s/C10=1 (b)

Grahic Jump Location
Fig. 9

Idealized force-controlled loading and unloading curves with Ẽ/C10/ε=0.25 and Ẽ/C10/ε=0.55

Grahic Jump Location
Fig. 10

Nominal electric field—stretch curves (a) and idealized voltage-controlled loading and unloading curves (b) for saturated model with various Ps/C10ε0

Grahic Jump Location
Fig. 11

Nominal stress–stretch curves with various saturated polarizations (a) and different initial voltages (b)

Grahic Jump Location
Fig. 12

Tensile curves (red) and step-up curves (blue) for VHB 4910 under different loading rate (a) 40 mm/min and (b) 80 mm/min

Grahic Jump Location
Fig. 13

Viscoelastic model consists of springs and dashpot

Grahic Jump Location
Fig. 14

Nominal stress–stretch curves with τv = 100 s and different k using viscoelastic model (a) and pseudo-elastic–viscoelastic model (b)

Grahic Jump Location
Fig. 15

Force–strain curves (a) and force–time curves (b) with different initial voltages and the comparison of fitting and experimental curves at 1.25 kV (c)

Tables

Errata

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