Analysis of effective properties of electroelastic composites using the self-consistent and asymptotic homogenization methods

The problem of the calculation of overall properties of a binary electroelastic fibre-reinforced composite is studied here, whose constituents are an elastic matrix and piezoelectric fibres that have transversely isotropic properties. Randomly positioned fibres as well as periodic distributed fibres are considered. The former case is dealt with by means of the self-consistent method and the latter one by asymptotic homogenization. Closed-form expressions are given for two variants of the self-consistent method, one in explicit form (effective field) and the other implicitly (effective medium). The former agree with the Mori–Tanaka equations. The equations derived using the asymptotic homogenization method are also explicit. It is shown that the three sets of effective coefficients satisfy analytically Schulgasser’s universal relations; the Milgrom–Shtrikman determinant is also explicitly satisfied by the effective field method variant. Overall properties are computed as a function of the fibre concentration. It is generally found that the properties calculated using the effective field self-consistent and homogenization methods are very close to each other for at least concentrations up to or near 0.3. In many cases the agreement is beyond that. Also the case when the constituents have either the same or opposite poling directions can be studied with the exact formulae. The antiplane strain related properties display interesting larger effects with opposite polings.