The crystal structure of common piezoelectric materials shows Dihexagonal symmetry. Hence, the following material symmetry conditions could be applied to the constitutive relationship:

(30.3)

After experimentally obtaining the material constants and using the material symmetry for hexagonal crystal structure, Eqns. (31.1 and 31.2) could be simplified and written as:

(30.4)

The electro-mechanical coupling is shown inside the bordered boxes in Eqn. (30.4). It may be noted that axes 1, 2 and 3 used for the electrical system are identical with x, y and z, corresponding to the mechanical system.