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

Effective anti-plane properties of piezoelectric fibrous composites

“…Application of the zeroth-order approximation yields a vector-matrix extension of the famous Clausius-Mossotti approximation (67). This result is in agree with [13] and [14] obtained in another form. The vector-matrix problem is decomposed into two scalar R-linear problems.…”

“…The vector-matrix extension (67) of the Clausius-Mossotti approximation is obtained (cf. [13] and [14]). The key point to get high-order approximations formulae for the effective constants is the decomposition of the vector-matrix problem into scalar R-linear problems.…”

“…The obtained results are valid for piezoelectric composites because of a common mathematical background. The application of self-consistent methods was extended by Levin et al [14] to 2-dimensional piezoelectric composites. One of the methods [14], based on the effective field, gave formulae for the effective constants in explicit form; the other, the effective medium, gave implicit formulae.…”

“…These conditions and formulae are analogous to Matheron [15] and Dykhne [16] ones deduced for scalar problems. It is worth noting that formulae obtained in the framework of the 2-dimensional theory of duality transformations [13,15,16] are exact, and formulae deduced by self-consistent methods [11][12][13][14] are approximate and hold only for dilute and weakly inhomogeneous composites. The theory of the self-consistent methods was systematically discussed by Kanaun and Levin [17]; its limitations were analyzed in [18].…”

Three-dimensional isofield micromechanics model for effective electrothermoelastic properties of piezoelectric composites

“…In this case, the poling and electric field directions are parallel to the fiber axis, causing a d 33 effect, which is useful in ultrasonic transducer applications. These micromechanics models have been developed based on the Voigt-type isofield method [Chan and Unsworth 1989;Smith and Auld 1991], the Mori-Tanaka method [Dunn and Taya 1993], the self-consistent method [Dunn and Taya 1993;Levin et al 2000], the generalized method of cells [Aboudi 1998], and the asymptotic homogenization method [Sabina et al 2001;Levin et al 2008].…”