Piezoelectric equations

[hborie]

Hello,

I try to understand how Abaqus resolve the piezoelectricity.

So I did a dynamic analysis with a peizoelectric patch on a shell. I put 1V on the top face of the patch.

At the first step, the material follow the equations (actuator) :

D = dT + εE
S = sT + dE

D : Electric displacement or induction
S : Strain
T : Stress
E : Electric field
d : dielectric constants
ε : permittivity
s : flexibility

It calculates the frequencies responses with this excitation and it gives some complex displacements.

From these displacements it calculates the strain and perform some equations (sensor):

D = εE + eS
T = cS - eE

e : dielectric constant
c : rigidity

From there, how Abaqus resolve the RCHG (Reactive electrical nodal charge)?
Does it integrate D and how does it perform it by gathering datas on nodes?

Is it how Abaqus does for these kind of analysis? Is there full documentation on the steps Abaqus performs?
I just want to understand the path of the software to write my thesis.

Sorry for my poor english, if you need more details on what I looking for, feel free to ask.
Thank you.

Sincerely,
H.B.