General assumptions for the stacking of material phases

Stacking Direction Transverse Plane coincidence weighted average weighted average coincidence 

These assumptions can be applied immediately in the directions ei and 2 of the cross-sectional plane of the fibers. As the constitutive relation of the considered piezoelectric materials exhibits only a partial electromechanical coupling, normal modes and each of the shear modes may be treated independently, as illustrated by Eqs. (4.19) to (4.21). In accordance with the considerations of Section 4.4.4, the notation with negated electric field strength and the associated constitutive submatrices E, Gi, and G2 will be utilized. 

The implications of Remark 5.5 are summarized in Table 5.2 for the stacking of material phases transverse to the fiber direction with respect to fields associated with the normal modes. While the macroscopic mechanical and electrostatic fields carry the usual denominations, the association with the individual phases is indicated by the superscripts / and m for fields in the fiber and matrix phase respectively. The normal mode constitutive relation of Eq. (4.19) 

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Table 5.1. General assumptions for the stacking of material phases with respect to the relation of macroscopic to microscopic mechanical and electrostatic fields.

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