Conversion of Piezoelectric coefficients

In summary, when double index notation is used, the values are placed in the correct positions, and triple index notation is used when some commercial software providers like Abaqus and MSC Marc.
  • #1
John Kai
2
2
Hello everyone,

I am interested on simulating the converse Piezoelectric effect of materials and I have given the mechanical (Youngs modulus and Poissoin's ratio) and electric material properties (Electric Permittivity, Piezoelectric coupling matrix etc). However from the literature I got double index notation, I am struggling to convert double index notation to triple index notation.

The double index notation from literature is as follows:

Double index notation

d11 d12 d13 d14 d15 d16 -------------- 0 0 0 0 21.3 0

d21 d22 d23 d24 d25 d26 -------------- 0 0 0 21.3 0 0

d31 d32 d33 d34 d35 d36 -------------- -2.6 -2.69 3.65 0 0 0

Triple index notation:
I would like to convert them to Triple index notation used by some commercial software providers like Abaqus and MSC Marc etc and is written as follows:

d11_1 d11_2 d11_3 -------------- 0 0 -2.6

d22_1 d22_2 d22_3 -------------- 0 0 -2.6

d33_1 d33_2 d33_3 -------------- 0 0 3.65

d12_1 d12_2 d12_3 -------------- 0 21.3 0

d23_1 d23_2 d23_3 -------------- 21.3 0 0

d31_1 d31_2 d31_3 -------------- 0 0 0

Am I doing the conversion correctly? Are the values placed in correct positions?
Double Index = Triple Index = Coupling Matrix Value
d11 = d11_1 =0
d21 = d11_2 = 0
d31 = d11_3 = -2.6
d12 = d22_1 = 0
d22 = d22_2 = 0
d32 = d22_3 = -2.6
.
...
...

d16 = d31_1 = 0
d26 = d31_2 = 0
d36 = d31_3 = 0

I am new to this filed and its kind of a big deal for me to understand all these conversions. Your feedback will be highly appreciated.
Kai
 
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  • #2
I think the index pairs are

##(1,1) = 1##
##(2,2) = 2##
##(3,3) = 3##
##(2,3) = (3,2) = 4##
##(1,3) = 5##
##(1,2) = (2,1) = 6##

There are factors of two thrown in so that

##C_{nmjk}S_{jk} = C_{ab}S_b##

things like

## S_{1,2} = \frac{1}{2} S_3##

when the dust clears. ##n, m, j, k## summed over 1 - 3 and ##a, b## summed 1-6.
This may help.

https://en.wikipedia.org/wiki/Piezoelectricity
 
  • #3
Dear Paul Colby,

I thnak you very much for your quick reply and explanation. I have already read the Wikipedia page briefly and will go through it again.
Thanks again!
 
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  • #4
This Piezo Systems site has some great images that may interest you.

e.g.
tech2intropiezotrans13.gif
 

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1. What is the conversion of piezoelectric coefficients?

The conversion of piezoelectric coefficients refers to the process of transforming the piezoelectric coefficients of a material from one system of units to another. This is done to make the coefficients more easily comparable and usable in different applications.

2. Why is the conversion of piezoelectric coefficients necessary?

The conversion of piezoelectric coefficients is necessary because different systems of units, such as the SI system and the CGS system, use different units to measure the same physical quantities. Therefore, converting the piezoelectric coefficients allows for easier comparison and use of the coefficients in different systems.

3. How is the conversion of piezoelectric coefficients done?

The conversion of piezoelectric coefficients is typically done using conversion factors or equations that relate the coefficients in one system to those in another system. These conversion factors are based on the unit conversions between the two systems.

4. What are the most commonly used systems for measuring piezoelectric coefficients?

The most commonly used systems for measuring piezoelectric coefficients are the SI system and the CGS system. The SI system is used in most countries around the world and is based on the meter-kilogram-second (mks) units. The CGS system is an older system and is based on the centimeter-gram-second (cgs) units.

5. Can the conversion of piezoelectric coefficients affect the accuracy of measurements?

Yes, the conversion of piezoelectric coefficients can affect the accuracy of measurements. This is because the conversion may involve rounding off numbers or using approximate values, which can introduce errors into the calculations. It is important to use accurate conversion factors and equations to minimize these errors.

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