OOF2: The Manual

Couplings:PiezoElectricity:Trigonal:D3
	6.4.1. Material Properties

Name

Couplings:PiezoElectricity:Trigonal:D3 — D3 piezoelectricity.

Details

Property Category: PiezoElectricity
Parameters:

dijk

Point group D3 (aka 32) piezoelectric tensor. Type: A D3Rank3Tensor object.
Fields: Voltage, Displacement
Fluxes: Total_Polarization, Stress

Discussion

PiezoElectricity is a coupling Property that makes a contribution to the Total_Polarization proportional to the Displacement gradient (strain), and a contribution to the Stress proportional to the Voltage gradient (electric field). The piezoelectric contribution to the Total_Polarization, $D$ , is

$D_m = C_{ijkl} d_{mkl} \epsilon_{ij}$

(6.94)

and its contribution to the Stress, $\sigma$ , is

$\sigma_{ij} = C_{ijkl}d_{mkl}\frac{\partial V}{\partial x_m}$

(6.95)

where $d$ is a third rank tensor given by the parameter dijk. In these equations, $V$ is the Voltage, $C_{ijkl}$ is the Material's elastic modulus, and $\epsilon$ is the geometric strain defined in Eqn. (6.2).

The different varieties of PiezoElectricity differ in the form of dijk, reflecting different crystal symmetries. The symmetry of dijkl should be compatible with the symmetry of the Material's elasticity, but this constraint is not enforced by OOF2.

A Material containing a PiezoElectricity Property must also contain an elasticity Property and an orientation Property. There is no such thing as isotropic piezoelectricity.


Couplings:PiezoElectricity:Trigonal:C3v		Couplings:PiezoElectricity:Trigonal:C3