Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Piezoelectric
Strain Behavior in Actuation DevicesTRACE: Tennessee Research and
Creative TRACE: Tennessee Research and Creative
Exchange Exchange
Spring 4-2004
Determining Limitations in the Ability of the ABAQUS Commercial
Determining Limitations in the Ability of the ABAQUS
Commercial
Finite Element Analysis Program to Accurately Predict Finite
Element Analysis Program to Accurately Predict
Piezoelectric Strain Behavior in Actuation Devices Piezoelectric
Strain Behavior in Actuation Devices
Christina Marie Spencer University of Tennessee - Knoxville
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Recommended Citation Recommended Citation Spencer, Christina Marie,
"Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Piezoelectric
Strain Behavior in Actuation Devices" (2004). Chancellor’s Honors
Program Projects.
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DETERMINING LIMITATIONS IN THE ABILITY OF THE ABAQUS COMMERCIAL
FINITE ELEMENT ANALYSIS PROGRAM TO
ACCURA TELY PREDICT PIEZOELECTRIC STRAIN BEHAVIOR IN ACTUATION
DEVICES
Reviewed by
NASA Langley Research Center March 31st, 2004
NASA-USRP Mentor Dr. Robert Bryant Advanced Materials and
Processing Branch
University of Tennessee Mentor Dr. AJ. Baker Department of
Mechanical, Aerospace, and Biomedical Engineering
ABSTRACT In order to better predict the actuation capabilities of
piezoelectric materials, a series of tests was performed on
piezoelectric material PZT SA and compared with computational
results performed using ABAQUS, a commercial finite element
analysis package. These experiments consisted of applying voltages
to basic PZT SA ceramic plates and PZT SA ceramic plates with
varying thicknesses of brass plates attached to the top of the
ceramic. A range of voltages was applied under quasi-isostatic
conditions and the resulting strain was measured at the top and
bottom of the actuator using commercial thin film strain gages. The
comparisons of experimental results to ABAQUS predicted results
show how accurate a commercial finite element analysis package is
with respect predicting the behavior of piezoelectric materials. By
looking at these comparisons, deficiencies in ABAQUS and other
similar programs can be recognized, and ways to overcome these
limitations can be developed. Such limitations include the
variation of piezoelectric constants with applied voltage,
piezoelectric hysteresis effects, and capturing the surface strain
in the plate from bending effects. Overcoming these deficiencies
will allow for faster and more accurate predictions of the geometry
and type of material needed for the more efficient use of
piezoelectric actuators.
INTRODUCTION The study of piezoelectric materials dates back to
1880 when they were discovered by Jaques and Pierre Curie. Their
discovery that some crystals became electrically charged when a
mechanical strain is applied to the crystal is known as the
piezoelectric effect. Since this discovery, testing and development
of these piezoelectric materials has led to the application of the
piezoelectric effect in many different generators and transducers.
The inverse piezoelectric effect, the deformation of these same
crystals when they are exposed to an electric field, has also been
used in a variety of sensors and actuators.
The development of these new products requires significant amounts
of testing and analysis. The need to accurately predict
experimental results using commercial finite element analysis (PEA)
programs is widely recognized because of the benefits accurately
predicted results will produce. Once a type of material can be
modeled using FEA, the need to perform actual experiments and the
high cost associated with these experiments can be limited. The
need to use a commercial FEA program arises when dealing with
companies and manufacturers that want fast results that can be
shared among colleagues using similar programs.
Currently, most FEA work in piezoelectric modeling has been done
using computer code written specifically for the chosen experiment.
While this provides more accurate results, it is not practical when
trying to determine geometry of complex actuators for larger
systems without performing experiments. Conversely, the
piezoelectric options in PEA programs like ABAQUS are vastly
oversimplified and do not accurately predict the experimental
results needed to replace testing.
PROBLEM The NASA Morphing project is developing a new type of
airplane wing that could use piezoelectric actuators. This
theoretical wing would have small holes in the downwind side of the
wing, allowing gas to be expelled from the wing when desired. This
idea has many aeronautical advantages, however it has some
disadvantages. One disadvantage is that the
1
device required to open and close the hole would prevent the wing
from being a wet wing and would also change the interior structure
of the wing. If a piezoelectric actuator could be used instead of
this device, the wet wing and structure of the wing would still be
feasible options for
the project.
Because of the obvious benefits of the piezoelectric actuator to
this project, this study was completed in order to better
understand how accurate ABAQUS results are and if the inaccuracies
could be accounted for using FEA techniques. If a somewhat accurate
prediction of a piezoelectric actuator can be developed,
considerable time and money can be saved when determining what size
and type of piezoelectric actuator would work best for this
wing.
METHOD OF SOLUTION In order to establish exactly what the ABAQUS
program can predict and what it's limitations are, a series of
experiments were performed, and the same experiments were modeled
using ABAQUS software. This was done in order to establish the
differences between the experimental results and the ABAQUS
predicted results. By comparing the two sets of results , the
limitations in the ABAQUS software become apparent. Once these
shortfalls are recognized, ways to vary the ABAQUS input to supply
the desired output can be created.
A series of experiments were performed in order to understand where
each problem with the ABAQUS modeling program occurs. For example,
the first experiment was a simple piezoelectric plate with an
electric field applied to it. By finding the differences in ABAQUS
predicted and experimental results for this simple experiment and
accounting for them, one step of the actuator modeling has been
complete. When moving to a more complicated actuation device, the
variation in the predicted and experimental results can be limited
because the variations in a simple piezoelectlic plate have already
been accounted for.
I. Simple Piezoelectric Plate Test The first test performed was on
a lead zirconate titanate (PZT) piezoelectric plate. Transparent
graph paper was used to align a Micromeasurements precision strain
gage in the center on the top of the plate. The strain gage was
attached using M-Bond 200 adhesive and a lOOg weight was set on top
of the strain gage while the glue dried. Strain gauge solder
telminals were also attached to the plates on either side of the
strain gauge, offset from the gage to avoid interference.
Next, lead wires were soldered to the solder terminals. One black
and one white wire were soldered to one of the terminals, and one
red wire was soldered to the other terminal. Lastly, a red wire was
applied to the top of the plate and a black wire applied to the
bottom of the plate using silver epoxy. These wires act as
electrodes to apply the electric field across the plate. The plate
was then placed in an oven to cure the epoxy. Once the epoxy was
dry and the instrumentation of the plate was complete, the plate
was poled by attaching the red and black wires to an amplifier and
running a direct current of appropriate magnitude through the
plate.
This instrumentation and poling process was completed for two
plates, Plate 1 and Plate 2, poling plate 1 at 1200 V and plate 2
at 2400 V. Plate 1 measured 4xlxO.015 inches and Plate 2 measured
3.375x2.25xO.03 inches. Once the plates were instrumented, Plate 1
was hooked up to
2
a Model 3800 Wide Range Strain Indicator from Vishay Instruments
Division, SIN 150658. Next, the plate was set on a small ceramic
block to allow the plate to be level. The red and black wires
attached to plate 1 were connected to a Trek PZD2000 High Voltage
Amplifier by the high voltage output and the ground output,
respectively. The amplifier input was attached to an Agilent 33120A
Frequency Generator.
To run the experiment, the frequency generator was set to output a
sine wave at 0.1 Hz. The High Z option on the generator was set.
The alternating current was applied at 100-1200 V in 100 V
increments. For each voltage, the strain indicator was set to zero,
the amplifier turned on, and the frequency increased from minimum
voltage to the desired voltage. Strain readings were taken using an
Agilent datalogger, and then the voltage was decreased and the
amplifier turned off. The strain indicator was re-zeroed, and the
process was repeated. After Plate 1 was finished, Plate 2 was
tested using the same process but the final voltage was 2400 V
instead of 1200 V, as Plate 2 is twice the thickness of Plate
1.
Finally, the same experiment was modeled using ABAQUS. A plate of
the same dimensions was created using C3D20E elements. The plate
was constrained by pinning one comer, which allowed for no movement
of that comer. The edge the comer belonged to was then fixed in the
1 and 3 directions, allowing no movement in either direction. The
opposite edge was also fixed in the 3 direction, simulating the
flat surface the plate was resting on.
Edge conslrained in the 1 and 3 directions
Figure 1: ABAQUS Constraints for Simple Piezoelectric Plate
Test
II. PZT -Brass Actuator After the first test was completed and the
experimental and predicted results compared, another experiment was
performed. This experiment used three PZT plates and attached a
brass plate of varying thickness to the top of each PZT plate. The
PZT plates used in this experiment had dimensions of
2.5xO.80xO.0080 inches, and the brass plates measured 2xO.80xO.00l,
0.003, or 0.005 inches. The same instrumentation and testing
process was used, but before applying the strain gages a brass
plate was attached to the top of the PZT plate. This was done using
3M
3
double stick tape 9461P. The strain gages were then applied to both
the top (brass) and bottom (PZT) of the actuator. The poling
voltage was 640 V, and the maximum alternating current applied was
400 V.
For the ABAQUS model, the same constraints as applied in the simple
piezoelectric plate test were used. The brass plates were attached
using the *TIE constraint, which ties the PZT plate surface to the
tape surface, and the tape surface to the brass surface.
III. THUNDER Actuator After the second test was completed, a test
of the more complicated THUNDER actuator was performed. The
experiment used a THUNDER actuator comprised of a stainless steel
layer, glue, piezoelectric plate, glue, and a thin aluminum layer.
The instrumentation and testing process was the same as used in the
previous two tests, except that four strain gages were applied to
both the top and the bottom of the THUNDER actuator, as shown
below.
Figure 2: Top of THUNDER Actuator with Strain gages applied
The THUNDER actuator was then modeled using ABAQUS. Because of
modeling complications, the glue and aluminum layers were not
modeled, only the stainless steel and PZT layers. The boundary
conditions were applied as in previous experiments. In order to
simulate the bent form of the THUNDER actuator, a force was applied
to the center of the actuator before applying a voltage across the
actuator. The set up is shown below.
4
DISCUSSION
I. Simple Piezoelectric Plate Test As shown below, the difference
between the ABAQUS predicted results and the experimental results
for this simple piezoelectric plate test consist of three main
problems: the hysteresis loop in the experimental results, a shift
in the experimental results, and the overall slope of the strain
versus electric field plot.
-- Experimental ~- Abaqus ---4.- Abaqus Exp D31
Plate 1 ~ 150 -,----------------, E <0
b T'-
X -c .~
Electric Field (x10"3 Vim)
b T'-
X -c
~ -60 +---~--~--~-----I
Electric Field (x10"3 Vim)
Figure 4: Simple Piezoelectric Plate Test Results at 200 Volts Peak
to Peak
Because the slope of these plots is the piezoelectric constant D31,
the difference in the slope can be accounted for by using the
experimental D31 for the ABAQUS program. This is shown by the red
in Figure 4. The shift in the experimental results is probably due
to residual strain induced by the poling of the plates. This and
the hysteresis loop are not easily accounted for, however the
ABAQUS results would give a general idea of the PZT plates induced
strain.
5
II. PZT -Brass Actuator The strain versus electric field data for
each actuator (0.001, 0.003, and 0.005 inch brass plates) is shown
below. When completing the ABAQUS simulation, the experimental
piezoelectric constant D31 was used in order to better match the
experimental data.
-- Experimental ~ ABAOUS
~ 200 T"""
~ -1000 -500 0 500 1000
Electric Field (x10"3 Vim)
E 80 60
-40 ..... -en -60 0 .....
Electric Field (x10"3 Vim)
Figure 5: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak
for a Brass Thickness of 0.001 inches
-- Experimental ABAOUS
~ 200 T"""
X 0 -c 'n; -200 ..... -en 0 -400 ..... .2 ~ -1000 -500 0 500
1000
Electric Field (x10"3 Vim)
~
Electric Field (x10"3 Vim)
Figure 6: PZT·Brass Actuator Test Results at 200 Volts Peak to Beak
for a Brass Thickness of 0.003 inches
6
~ 200 ..- x 0 --c
.(ij -200 ..... -(/) 0 -400 ..... u ~ -1000 -500 0 500 1000
Electric Field (x1 ()1\3 Vim)
E -E co < 0 ..- x --c
.(ij ..... -(/) 0 ..... u ~
60 40 20 o
Electric Field (x10"3 Vim)
Figure 7: PZT-Brass Actuator Test Results at 200 Volts Peak to Beak
for a Brass Thickness of 0.005 inches
The main shortfalls of the ABAQUS program concerning these
Brass-PZT actuators are the inability of ABAQUS to capture even the
direction at the top of the actuator's strain and the inability of
ABAQUS to show the increased strain and therefore the increased
piezoelectric constant D31 for the bottom of the actuator. Upon
closer inspection of this effective D31 for the experimental and
ABAQUS results, the ABAQUS effective D31 is virtually the same as
the actual D31. The experimental D31, however, increases
dramatically which causes the increased strain in the
material.
Another interesting feature of the experimental data is the fact
that the slope of the strain versus electric field plot at the top
of the actuator is in the opposite direction for the 0.001 inch
brass plate actuator as it is in the 0.003 and 0.005 inch brass
plate actuators. This is probably because the 0.001 inch brass
plate is so thin that the piezoelectric material is stretching the
brass, where in the other two actuators, the brass is thick enough
to induce actuation. This theory is supported by the fact that the
slope of the strain versus electric field plot is less in the 0.001
inch actuator than in the 0.003 and 0.005 inch actuators.
7
E Bottom of Actuator (PZT) u·c> -C\I u..-
0..---- --------,
::::<fJ We o
Electric Potential (Volts)
E u·c> -C\I u..- ~b OT"" N x Q)- O:::T""
('t)
20
o
-20
Electric Potential (Volts)
Figure 8: PZT -Brass Actuator Effective Piezoelectric Constant for
a Brass Thickness of 0.005 inches
III. THUNDER Actuator Experimental Results of the THUNDER Testing
are shown in Appendix 1. Because of time constraints, successful
ABAQUS modeling of the THUNDER device was not achieved at the time
of this report.
CONCLUSION From these initial results, it is clear that more work
needs to be done to achieve a successful model of piezoelectric
materials using ABAQUS. While it is clear that the ABAQUS program
does not present an ideal representation of piezoelectric
materials, it can be modified to present more accurate results.
This study has identified the most significant problems of ABAQUS
modeling of piezoelectric materials in relation to the strain
measurements of piezoelectric actuators. They are as follows:
piezoelectric hysteresis loops, the strain shift caused by poling
of piezoelectric materials, the increased effective piezoelectric
constant in a simple piezoelectric actuator, and the strain
measurements on the top of a simple piezoelectric actuator.
Some if not all of these problems with ABAQUS can be overcome using
various modeling techniques. For example, an initial strain based
on the poling of the material could be applied to the material in
order to account for the strain shift caused by poling of
piezoelectric materials. More experimental studies of simple
actuators could yield a formula to determine how much to increase
the effective piezoelectric constant by to obtain similar stress
results. Other methods could be employed to simulate hysteresis
loops and to obtain accurate results for the strain on the top of a
simple piezoelectric actuator.
8
REFERENCES
"Load characterization of high displacement piezoelectric actuators
with various end conditions." Sensors and Actuators April 2001.
19-24
"Piezoelectric strain in lead zierconate titante ceramics as a
function of electric field, frequency, and dc bias." Journal of
Applied Physics. 15 July 2003. Volume 94, number 2,1155-1162
Wanders, l.W. Piezoelectric Ceramics. Eindhoven; N.V. Philips,
April 1991
9
Thunder Wafer Instrumentation
Top Gage 1 (Uppe, Left) Gage 2;;:::: Gage 3 Uppe, Right
~I I Gage 4 (Lower Left)
Bottom (plate flipped horizontally)
Gage 5 (Upper Left) Gage 7 (Upper Right)
Test 2: 100 V with 150 DC Bias 100V, 150 DC Bias
0.0001 -,------------ - --- --- -------------,
Y = 1.6607E-ll x + 3.2009E-0
0.00005
r==~;;;;;;;;;;;~;;;;;;;;~:::_.~Y~-=~9~.36~1~0~E-~'2~X~+~2.~466;5E~-05~
o y = -5.065OE-12x + 1.2783E-05
4 0 500000 600000 700000 800000 900000 1 OOOOOOy = \ 'BWg_ 121
22~e888~:(J -0.00005 -\-_ ________________
--'-.....:..:::::..:=:.::..c=-:...:..:==::....::..=j
-0.0002
-0.00025
-0.0003
Bottom Upper Lelt (transverse) - Bottom Upper Rig,t
Top Upper Left (transverse) - Top Upper Rig,t - Bottom Lower Left -
Bottom Center - Top Lower Left
y = -8.0069E-llx - 3.1943E-
y = -1.3911E-1Ox - 5.2621E-05
f------------- --- - - --l - To Center
4 5 6 7
Determining Limitations in the Ability of the ABAQUS Commercial
Finite Element Analysis Program to Accurately Predict Piezoelectric
Strain Behavior in Actuation Devices
Recommended Citation