The linear piezoelectric equations as presented in About Piezoelectric Materials with engineering strains are valid if the model undergoes only relatively small deformations. As soon as the model contains larger displacements or rotations, these equations produce spurious strains that result in an incorrect solution. To overcome this problem, so-called large deformation piezoelectric equations are required.
where S is the second Piola–Kirchhoff stress;
ε is the Green–Lagrange strain,
Em and
Pm are the electric field and electric polarization in the material orientation;
I is the identity matrix; and
cE,
e, and
εrS are the piezoelectric material constants. The expression within parentheses equals the dielectric susceptibility of the solid:
where C is the right Cauchy–Green tensor
where F is the deformation gradient;
J is the determinant of
F; and
ρv and
ρV are the volume charge density in spatial and material coordinates, respectively. The deformation gradient is defined as the gradient of the present position of a material point
x = X +
u:
The Piezoelectricity, Solid Interface can be coupled with the Moving Mesh (ALE) interface in a way so that the electrical degrees of freedom are solved in an ALE frame. This feature is intended to be used in applications where a model contains nonsolid domains, such as modeling of electrostatically actuated structures. This functionality is not required for modeling of piezoelectric or other solid materials.
