Stacking of material phases in the axial directions

Remark 5.4. Mechanical and electrostatic fields are assumed to be homogeneous throughout the individual material phases. 

As the entire composite structure happens to be assembled from simplified representative volume elements by symmetric completion and repetition, the edges have to remain straight and parallel in any event. Transferred to the mechanical and electrostatic fields, this requirement may be fulfilled on the grounds of the following assumption  

Remark 5.5. The macroscopic mechanical and electrostatic fields either coincide with field quantities found to be identical in all material phases or result from the average of field quantities in the individual material phases weighted by their directional fraction in accordance with the scheme of Table 5.1. 

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. 

---