Micro-Electromechanics with Equivalent Inclusions

Remark 5.2. The subsequent discussion of micro-electromechanical approaches to determine the macroscopic constitutive properties of a composite will be concentrated on properties within the following categories  

Typically, the fiber material is at most transversely isotropic, Eq. (4.17) with Eqs. (4.3), (4.8), and (4.18), while the matrix material is isotropic, Eq. (4.17) with Eqs. (4.4), (4.9), and vanishing piezoelectric moduli. The subsequent theories are not confined to such a behavior. However, it will be presumed that the distinguished axes are aligned. Deviating cases may be considered in conjunction with an appropriate transformation, see Section 3.2.5. In accordance with the considerations of Section 4.4.4, the notation with a negated electric field strength will be utilized throughout the entire chapter. 

The micro-electromechanical methodology stemming from the category of the Theory of Elasticity to be presented in this section is capable of modeling inclusions of ellipsoidal geometry. Such a description of the inclusion geometry allows us to consider fibrous and lamellar inclusions by means of one or two semiaxes approaching infinity, respectively. 

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Micro-Electromechanics with Equivalent Inclusions 81 5.3.4 Non-Dilute Concentrations... 

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