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Parameter Definitions

Permittivity

The permittivity, or relative dielectric constant, , is a measure of the polarizability of the material. The directionality of the permittivity is expressed by tensor components, whereby the same component indexes are used as for th electric field and dielectric displacement.
For example,

• ₃₃ T
  describes the permittivity value in the polarization direction (direction 3) when an electric field is applied also in the polarization direction, under conditions of constant mechanical stress (T = 0: “free” permittivity)

• ₁₁S
  is the electric field and dielectric displacement in direction 1, perpendicularto to the polarization direction at constant deformation S = 0: clamped permittivity)

Piezoelectric charge constant d_ij

The piezoelectric charge or strain constant d is a measure of the electric charge induced in response to a mechanical stress, or the achievable mechanical strain when an electric field is applied (T = constant). For example,

• d₃₃
  is the charge density developed per mechanical stress, or, alternatively, strain developed per unit of electric field strength, all in the polarization direction.

Piezoelectric voltage constant g_ij

The piezoelectric voltage constant g defines the ratio of the electric field strength E to the effective mechanical stress T. If one divides the respective piezoelectric charge constants d_ij by the corresponding permittivity value one gets the corresponding g_ij constant For example,

• g₃₁
  describes the electric field induced in direction 3 by a mechanical stress acting in direction 1.

Elastic constant s_ij

The elastic constant or compliance s is a measure of ij the ratio of the relative deformation S to the mechanical stress T. Because it depends on the interaction of mechanical and electrical energy, the electrical boundary conditions must be taken into consideration.
For example,

• S₃₃^E
  describes the ratio of the mechanical strain in direction 3 to the mechanical stress in direction 3, with constant electric field (for E = 0: short circuit)

• S₅₅^D
  is the ratio of a shear strain to the effective shear stress with constant dielectric displacement for D = 0:open circuit)

Note:
Young’s modulus Y_ij, which is often used in the English speaking world, is the reciprocal of the compliance constant.