Dear Manish,

These are the list of structural-electrical simulations that I'm aware of

Piezoresistive

Electroelastic

Piezoelectric

If you want to add Thermal physic to the constitutive equation then we can add these to the list as well.

Structural-Thermoelastic

Thermal-Piezoelectric

As always, Please recommend this answer if it worked for you and let other people to find the correct answers faster.

Here i asked different form of electro-elastic coupling only not different form of interaction. I need interaction of electric and mechanical coupling only i.e., renowned as electro-elastic coupling. Is there any other forms of electro-elastic coupling ?

As far as I know, we have only two forms which you already mentioned. Electroelastic for positive electric charge and Piezoelectric for negative electric charge.

As far as I know , there is no such positive and electric charge based constitutive relation of linear piezoelectric material.

There are two effects based on non-centrosymmetric nature of ceramic (for eg, quartz, PZT,etc ) based crsytal i.e., Converse piezoelectric effect and Direct piezoelectric effect.

Converse piezoelectric effect : The application of an electrical field creates mechanical deformation in the crystal.

{stress} = [C] * {strain} + [d] *{E};

Direct piezoelectric effect : The electric charge develops as a result of the applied mechanical stress.

{D} = [d]*{strain} + [permitivitty]* {E} I didn't understand what you meany by piezoelectric and electro-elastic ?

I think there is :).

The reaction solution for Electroelastic coupled-field is positive electric charge, whereas negative electric charge for Piezoelectric coupled-filed. Below you can find the refrence to that.

https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_SOLID226.html

If you say "There is no such positive and electric charge based constitutive relation of linear piezoelectric material." Please provide a refrence.

I think we are not talking in same language. By the way. I put the contitutive equation with explanation of each parameter for who ever wants to know what are these parameters.

Can you explain or cite any paper or book ?

Read this book :

Erturk, A. and Inman, D.J., 2011. Piezoelectric energy harvesting. John Wiley & Sons.

Jaffe, Bernard. Piezoelectric ceramics. Vol. 3. Elsevier, 2012.

Try this link :

https://en.wikipedia.org/wiki/Piezoelectricity

The Images and equation's you shared I already mentioned. Please provide the explanation of

Electro-elastic constitutive relation ?

Piezoelectric constitutive relation ?

Thank you :)

I sent you a link in my previous comment. Check the reaction solution column in the second table. Then you will have good sense of positive and negative. Do I have to read the whole book to find what you are saying or you can be more specific??

you shared but whiout any explanaition of each parameter. I just wanted to complete your explanation:).

Well i have to study to answer the ANSYS based definition of electo-elastic and piezoelectric constitutive provided by you :

https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_SOLID226.html

But you can find the definition of Converse and direct piezoelectric effect anywhere in wikepedia or any text book of piezoelectricity available to you. But nowhere its mentioned that its positive or negative electric charge based relation.

If you read the ANSYS based definition of electroelastic and piezoelectric.

Can you explain the difference mentioned in the link (

Table 223.4:  PLANE223 Material Properties and Material Models )

Electroelastic : Coupling not mentioned

Piezoelectric : Coupling mentioned.

https://www.sharcnet.ca/Software/Ansys/17.0/en-us/help/ans_elem/Hlp_E_PLANE223.html#plane223.tab.2.ft.3

Well, that is your choice.

Here are more information on how we can define material properties in ansys for performing this coupled-field analysis. I know that you may know this :). I just provided for whoever wants to know more about this kind of simulation.

Hamidreza Ahmadi Moghaddam

Nice information shared by you. But if you have the answer of electro-elastic constitutive relation and Piezoelectric constitutive relation mentioned anywhere . Then please share. I am very interested to know the answer :)

Would you please say what do you mean by "constitutive relation". Do you mean how we conclude the equations??I mean are you looking after derivation?

According to you what I understand

Converse piezoelectric effect : Electro-elastic

Direct piezoelectric effect :Piezoelectric

Is it true ?

Constitutive relations for linear piezoelectric material:

Converse piezoelectric effect : The application of an electrical field creates mechanical deformation in the crystal.

{stress} = [C] * {strain} + [d] *{E};

Direct piezoelectric effect : The electric charge develops as a result of the applied mechanical stress.

{D} = [d]T*{strain} + [epsilon]* {E}

where d is the piezoelectric coefficients matrix of size (6X3); epsilon is the permitivitty matrix of size (3X3) ; C is the stiffness matrix of size (6X6); E is the electric field of size (3X1); stress/strain is a vector of size (6X1); D is the electric displacement vector of size (3X1);

It is absolutely true. The process of piezoelectric is completely reversible. I did a project for designing a MEMS device long time ago and found these two documents from there. Hope these help as well.

I know about the process of piezoelectric is completely reversible. That's why I mentioned about converse and direct piezoelectric effect. But I am not aware that it is also called Electro-elastic and Piezoelectric effect. I never read anywhere and even i couldn't find in the document shared by you. I don't know how far it is correct. Still I find it debatable.

Recently, I found one such coupling named as " flexoelectric coupling " .