The constitutive equation of Piezoelectric materials ?

[ThangMMM]

I'm studying about piezoelectric material. The electro - mechanical property of this material can be described by the following constitutive equation:

Sij is the compliance matrix, and dmi is the piezoelectric constant for the materials

The matrix form of the equation:

Applying this equation for PZT (lead zirconate titanate) materials with tetragonal perovskite structure, some of these above Sij and dmi can be equal, or zero. The equation becomes:

I'm concerning about why S31 = S32 = S13 = S23 and S66 = 2(S11 - S12) ??

When I'm reading some documents about PZT, they usually classify PZT into PZT-4, PZT-5, etc (like this: http://www.efunda.com/Materials/piezo/material_data/matdata_index.cfm ). What does these number after it means ?

thank you very much\..

 

[Chestermiller]

I'm studying about piezoelectric material. The electro - mechanical property of this material can be described by the following constitutive equation:

View attachment 125487

Sij is the compliance matrix, and dmi is the piezoelectric constant for the materials

The matrix form of the equation:

View attachment 125488

Applying this equation for PZT (lead zirconate titanate) materials with tetragonal perovskite structure, some of these above Sij and dmi can be equal, or zero. The equation becomes:

View attachment 125489

I'm concerning about why S31 = S32 = S13 = S23 and S66 = 2(S11 - S12) ??

These conditions must mean that PZT has anisotropic material symmetries such that it is transversely isotropic.