Stacking of material phases with respect to normal modes

Direction Stress/Ei. Fiux Density Strain/Ei. Eieid Strength 

Furthermore, those mechanical and electrostatic fields that are assumed to be a weighted average, as stated in Table 5.2, may be arranged collectively. Then the vectors of the phase specific fields can be replaced by substitution of Eqs. (5.18a) and (5.18b), respectively  

These still partially inverted macroscopic constitutive relations with the weighted average of material properties of both phases comprised in the matrices Fi and F2, may be reverted to the original form of the normal mode constitutive relations  

The coefficients of the constitutive matrices and E, as of Eq. (4.19), thus stem from the matrices Fi and F2, respectively. They can be derived from each other by interchanging the indices 1 and 2 of directional fiber fractions as well as constitutive coefficients of fiber and matrix material again indicated by the superscripts / and m. So the presentation of these coefficients can be confined to the matrix E as a result of the stacking of constituents in the ei-direction. The entries of the principal diagonal contained therein are 

As the remaining mechanical and piezoelectric coupling coefBcients directly affect the stacking direction, no additional terms appear but series-connection-like modifications of phase properties arise within a parallel connection  

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Table 5.2. Assumptions for the stacking of material phases with respect to normal modes.

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