By employing recent results (Lopez-Pamies, O., 2014, “Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics,” J. Mech. Phys. Solids, 64, p. 6182 and Spinelli, S. A., Lefèvre, V., and Lopez-Pamies, O., “Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit,” J. Mech. Phys. Solids, 83, pp. 263–284.) on the homogenization problem of dielectric elastomer composites, an approximate solution is generated for the overall elastic dielectric response of elastomers filled with a transversely isotropic distribution of aligned spheroidal particles in the classical limit of small deformations and moderate electric fields. The solution for such a type of dielectric elastomer composites is characterized by 13 (five elastic, two dielectric, and six electrostrictive) effective constants. Explicit formulae are worked out for these constants directly in terms of the elastic dielectric properties of the underlying elastomer and the filler particles, as well as the volume fraction, orientation, and aspect ratio of the particles. As a first application of the solution, with the objective of gaining insight into the effect that the addition of anisotropic fillers can have on the electromechanical properties of elastomers, sample results are presented for the case of elastomers filled with aligned cylindrical fibers. These results are confronted to a separate exact analytical solution for an assemblage of differential coated cylinders (DCC), wherein the fibers are polydisperse in size, and to full-field simulations of dielectric elastomer composites with cylindrical fibers of monodisperse size. These results serve to shed light on the recent experimental findings concerning the dielectric elastomers filled with mechanically stiff fibers. Moreover, they serve to reveal that high-permittivity liquid-like or vacuous fibers—two classes of filler materials yet to be explored experimentally—have the potential to significantly enhance the electrostriction capabilities of dielectric elastomers.

References

References
1.
Lopez-Pamies
,
O.
,
2014
, “
Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics
,”
J. Mech. Phys. Solids
,
64
, pp.
61
82
.
2.
Spinelli
,
S. A.
,
Lefèvre
,
V.
, and
Lopez-Pamies
,
O.
, “
Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit
,”
J. Mech. Phys. Solids
,
83
, pp.
263
284
.
3.
Dorfmann
,
A.
, and
Ogden
,
R. W.
,
2005
, “
Nonlinear Electroelasticity
,”
Acta Mech.
,
174
(
3–4
), pp.
167
183
.
4.
Stratton
,
J. S.
,
1941
,
Electromagnetic Theory
,
McGraw-Hill
,
New York
.
5.
Toupin
,
R. A.
,
1956
, “
The Elastic Dielectric
,”
J. Ration. Mech. Anal.
,
5
, pp.
849
915
.
6.
Tian
,
L.
,
Tevet-Deree
,
L.
,
deBotton
,
G.
, and
Bhattacharya
,
K.
,
2012
, “
Dielectric Elastomer Composites
,”
J. Mech. Phys. Solids
,
60
(
1
), pp.
181
198
.
7.
Walpole
,
L. J.
,
1981
, “
Elastic Behavior of Composite Materials: Theoretical Foundations
,”
Adv. Appl. Mech.
,
21
, pp.
169
242
.
8.
Wissler
,
M.
, and
Mazza
,
E.
,
2007
, “
Electromechanical Coupling in Dielectric Elastomer Actuators
,”
Sens. Actuators A
138
(
2
), pp.
384
393
.
9.
Di Lillo
,
L.
,
Schmidt
,
A.
,
Bergamini
,
A.
,
Ermanni
,
P.
, and
Mazza
,
E.
,
2011
, “
Dielectric and Insulating Properties of an Acrylic DEA Material at High Near-DC Electric Fields
,”
Proc. SPIE
,
7976
, p.
79763B
.
10.
Willis
,
J. R.
,
1977
, “
Bounds and Self-Consistent Estimates for the Overall Moduli of Anisotropic Composites
,”
J. Mech. Phys. Solids
,
25
(
3
), pp.
185
202
.
11.
Huang
,
C.
, and
Zhang
,
Q. M.
,
2004
, “
Enhanced Dielectric and Electromechanical Response in High-Dielectric Constant All-Polymer Percolative Composites
,”
Adv. Funct. Mater.
,
14
(
5
), pp.
501
506
.
12.
Huang
,
C.
,
Zhang
,
Q. M.
,
Li
,
J. Y.
, and
Rabeony
,
M.
,
2005
, “
Colossal Dielectric and Electromechanical Responses in Self-Assembled Polymeric Nanocomposites
,”
Appl. Phys. Lett.
,
87
(
18
), p.
182901
.
13.
Liu
,
H.
,
Zhang
,
L.
,
Yang
,
D.
,
Yu
,
Y.
,
Yao
,
L.
, and
Tian
,
M.
,
2013
, “
Mechanical, Dielectric, and Actuated Strain of Silicone Elastomer Filled With Various Types of TiO2
,”
Soft Mater.
,
11
(
3
), pp.
363
370
.
14.
Wang
,
S.
, and
Mark
,
J. E.
,
1990
, “
Generation of Glassy Ellipsoidal Particles Within an Elastomer by In Situ Polymerization, Elongation at an Elevated Temperature, and Finally Cooling Under Strain
,”
Macromolecules
,
23
(
19
), pp.
4288
4291
.
15.
Meddeb
,
A. M.
, and
Ounaies
,
Z.
,
2012
, “
Nano-Enhanced Polymer Composites for Energy Storage Applications
,”
Proc. SPIE
,
8342
, p.
834207
.
16.
Lu
,
T.
,
Huang
,
J.
,
Jordi
,
C.
,
Kovacs
,
G.
,
Huang
,
R.
,
Clarke
,
D. R.
, and
Suo
,
Z.
,
2012
, “
Dielectric Elastomer Actuators Under Equal-Biaxial Forces, Uniaxial Forces, and Uniaxial Constraint of Stiff Fibers
,”
Soft Matter
,
8
(
22
), pp.
6167
6173
.
17.
Li
,
J. Y.
, and
Rao
,
N.
,
2004
, “
Micromechanics of Ferroelectric Polymer-Based Electrostrictive Composites
,”
J. Mech. Phys. Solids
,
52
(
3
), pp.
591
615
.
18.
Siboni
,
M. H.
, and
Ponte Castañeda
,
P.
,
2013
, “
Dielectric Elastomer Composites: Small-Deformation Theory and Applications
,”
Philos. Mag.
,
93
(
21
), pp.
2769
2801
.
19.
Pelrine
,
R.
,
Kornbluh
,
R.
, and
Joseph
,
J. P.
,
1998
, “
Electrostriction of Polymer Dielectrics With Compliant Electrodes as a Means of Actuation
,”
Sens. Actuators A
,
64
(
1
), pp.
77
85
.
20.
Park
,
J.
,
Wang
,
S.
,
Li
,
M.
,
Ahn
,
C.
,
Hyun
,
J. K.
,
Kim
,
D. S.
,
Kim
,
D. K.
,
Rogers
,
J. A.
,
Huang
,
Y.
, and
Jeon
,
S.
,
2012
, “
Three-Dimensional Nanonetworks for Giant Stretchability in Dielectrics and Conductors
,”
Nat. Commun.
,
3
, p.
916
.
21.
López Jiménez
,
F.
, and
Pellegrino
,
S.
,
2012
, “
Constitutive Modeling of Fiber Composites With a Soft Hyperelastic Matrix
,”
Int. J. Solids Struct.
,
49
(
3–4
), pp.
635
647
.
22.
Wang
,
Q.
,
Suo
,
Z.
, and
Zhao
,
X.
,
2012
, “
Bursting Drops in Solid Dielectrics Caused by High Voltages
,”
Nat. Commun.
,
3
, p.
1157
.
23.
Fassler
,
A.
, and
Majidi
,
C.
,
2015
, “
Liquid-Phase Metal Inclusions for a Conductive Polymer Composite
,”
Adv. Mater.
,
27
(
11
), pp.
1928
1932
.
24.
Lefèvre
,
V.
, and
Lopez-Pamies
,
O.
,
2014
, “
The Overall Elastic Dielectric Properties of a Suspension of Spherical Particles in Rubber: An Exact Explicit Solution in the Small-Deformation Limit
,”
J. Appl. Phys.
,
116
(
13
), p.
134106
.
25.
Hashin
,
Z.
, and
Rosen
,
B. W.
,
1964
, “
The Elastic Moduli of Fiber-Reinforced Materials
,”
ASME J. Appl. Mech.
,
31
(
2
), pp.
223
232
.
26.
Avellaneda
,
M.
,
1987
, “
Iterated Homogenization, Differential Effective Medium Theory and Applications
,”
Commun. Pur. Appl. Math.
,
40
(
5
), pp.
527
554
.
27.
Milton
,
G. W.
,
1985
, “
The Coherent Potential Approximation is a Realizable Effective Medium Scheme
,”
Commun. Math. Phys.
,
99
(
4
), pp.
463
500
.
28.
Milton
,
G. W.
,
2002
,
The Theory of Composites
,
Cambridge University Press
,
Cambridge, UK
.
29.
Bland
,
D. R.
,
1965
,
Solutions to Laplace's Equation
,
Routledge and K. Paul
,
London
.
30.
Christensen
,
R. M.
, and
Lo
,
K. H.
,
1979
, “
Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models
,”
J. Mech. Phys. Solids
,
27
(
4
), pp.
315
330
.
31.
Hill
,
R.
,
1964
, “
Theory of Mechanical Properties of Fibre-Strengthened Materials: 1. Elastic Behaviour
,”
J. Mech. Phys. Solids
,
12
(
4
), pp.
199
212
.
32.
Hashin
,
Z.
,
1979
, “
Analysis of Properties of Fiber Composites With Anisotropic Constituents
,”
ASME J. Appl. Mech.
,
46
(
3
), pp.
543
550
.
33.
Moraleda
,
J.
,
Segurado
,
J.
, and
LLorca
,
J.
,
2009
, “
Finite Deformation of Incompressible Fiber-Reinforced Elastomers: A Computational Micromechanics Approach
,”
J. Mech. Phys. Solids
,
57
(
9
), pp.
1596
1613
.
34.
abaqus Version 6.11 Documentation, 2011, Dassault Systemes Simulia Corp., Providence, RI.
35.
matlab Version 8.3 Documentation, 2014, Mathworks, Natick, MA.
This content is only available via PDF.
You do not currently have access to this content.