Piezoelectric coupled governing equations doubt

[jatin1990]

Hi , can anybody make me sense of these equation on which i am striking my head for last 2 months. I am trying to understand piezoelectric effect. And in process of which i came to see so called strain based form of equations related to direct(Equation no.2) and reverse(Equation no. 1) piezoelectric effect(attached pic). Can anybody clear my doubt, as if we want to produce the direct effect(Stain to electric field) then we have to go with the 2nd equation. But in the 2nd equation we have two unknown variable matrix i.e. {E} and {D} . How we can solve two unknown variables with the help of a one equation(assuming we can't use 1st equation as it is meant for only reverse effect). Same confusion arising when i tries to make any sense out of 1st equations while following inverse effect.
Thank you a lot.

 

[nasu]

If you want to find the strain produced by an electric field then it's better to use a different set of constitutive equations. Of course, then you will need a different set of tensor components.For example there is
{S}=s^D{T} +g {D}
If you apply electric field only (no mechanically induced strain) then you have
{S}=g {D}
and you can know the strain if you know the electric displacement.

From your set of equations, you can find the stress in presence of an external electric field.