High-strain active materials often exhibit relaxation in their response to an electric or magnetic field. This phenomenon has been previously described by a loss factor (tangent of the phase shift). However, the loss factor cannot express frequency-dependent, nonperiodic time-dependent, or nonlinear responses, therefore more fundamental material constants are needed. We present a phenomenological model that describes the time- and frequency-dependent behavior of electromechanically (piezoelectric and electrostrictive) and magnetomechanically (magnetic shape memory and magnetostrictive) active materials. Expanding rheology, we introduce electrorheological and magnetorheological models incorporating time constants corresponding not only to the viscoelastic response, i.e., strain versus stress, but also: (1) polarization or magnetization versus field, (2) strain versus polarization or magnetization, (3) ferro- and antiferroelectric, ferro- and antiferromagnetic, or ferroelastic domain switching under applied field and/or stress. A single set of constitutive equations is obtained that can describe pure and mixed cases of ferroic, antiferroic, and nonferroic response. The simulated behavior agrees well with experimental data for both polycrystalline piezoelectrics and high electromechanical strain single crystals.

1.
T. Ikeda, Fundamentals of Piezoelectricity (Oxford University, Press, Oxford, 1996).
2.
S.-E.
Park
and
T. R.
Shrout
,
J. Appl. Phys.
82
,
1804
(
1997
).
3.
K. Uchino, Piezoelectric Actuators and Ultrasonic Motors (Kluwer Academic, Boston, MA, 1997).
4.
H.
Szymczak
,
J. Magn. Magn. Mater.
200
,
425
(
1999
).
5.
L. E.
Cross
,
Ferroelectrics
151
,
305
(
1994
).
6.
R. S. Lakes, Viscoelastic Solids (CRC, Boca Raton, FL, 1999).
7.
K. Uchino and S. Hirose, IEEE Trans. Ultrason. Ferroelectr. Freq. Control (to be published).
8.
D. Mayergoyz, Mathematical Models of Hysteresis (Springer, New York, 1991).
9.
R. C.
Smith
,
Proc. SPIE
3041
,
243
(
1997
).
10.
J. C.
Piquette
and
S. E.
Forsythe
,
J. Acoust. Soc. Am.
106
,
3317
(
1999
).
11.
P. J.
Chen
and
S. T.
Montgomery
,
Ferroelectrics
23
,
199
(
1980
).
12.
Y.-M.
Chiang
,
G. W.
Farrey
, and
A. N.
Soukhojak
,
Appl. Phys. Lett.
73
,
3683
(
1998
).
13.
J.
Zhao
and
Q. M.
Zhang
,
ISAF ’96 Proceedings of the Tenth IEEE International Symposium
Applied Ferroelectrics.
,
2
,
971
(
1996
).
14.
B. G.
Potter
Jr.
,
V.
Tikare
, and
B. A.
Tuttle
,
J. Appl. Phys.
87
,
4415
(
2000
).
15.
C. S.
Lynch
,
Acta Mater.
44
,
4137
(
1996
).
16.
R. C.
O’Handley
,
J. Appl. Phys.
83
,
3263
(
1998
).
This content is only available via PDF.
You do not currently have access to this content.