Non-Homogeneous Electrostatic Fields

Direction Stress/El. Flux Density Strain/El. Field Strength 

To proceed just like in the other stacking cases, the constitutive relation of Eq. (4.19) may be rewritten for fiber and matrix material as follows  

those mechanical and electrostatic fields that originally have been assumed to be a weighted average, as stated in Table 5.4, may be arranged collectively and Eqs. (5.25) inserted  

This still partially inverted macroscopic constitutive relation may be reverted correspondingly to the original form of the normal mode constitutive relations  

Unlike the procedure laid out above, which introduces the factor C3, in the publications of Bent and Hagood [14,15] and Bent [13], the fraction is set to one only for the mechanical fields, while it is retained for the electrostatic fields. The resulting constitutive matrix of Eq. (5.27b) therefore becomes non-symmetric with respect to the piezoelectric coupling coefficients. Since the undermost line of the normal mode constitutive relation is not used there any further, this has no consequences. 

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