The fundamental equations of piezoelectricity are given by

	(30.1)
	(30.2)

where, the subscripts i , j , k , l = 1, 2, 3 denotes tensorial indices.
The stress tensor is represented by σ , S is the strain tensor, E is the electric field intensity and D is the electric displacement field. The elastic stiffness matrix is denoted by the symbol C^E, where the superscript E denotes that the elastic constant is measured under constant electric field (henceforth, the superscript will not be shown explicitly for the sake of brevity); e is the piezoelectric stress-charge matrix and ε the permittivity matrix, similar to C , is measured under constant strain-condition. The details of the axes are shown in Fig 30.2.

Figure 30.2: A piezoelastic plate with electrodes and poling direction