High-order contrast bounds for piezoelectric constants of two-phase fibrous composites

The constructive theory of analytical higher-order contrast bounds for the effective constants of dispersed conducting and piezoelectric fibrous composites is developed. The lower-order bounds, e.g., Wiener and Hashin-Shtrikman bounds, are universal for composites but do not take into account interactions among inclusions corresponding to their location. To study the variety of dispersed random composites, we use computationally effective structural sums directly relating the location of inclusions to the effective constants. The present paper is the first report where the structural sums are applied to higher-order contrast bounds instead of the virtually impossible in computation multipoint correlation functions. We concentrate our attention on two-phase conducting fibrous composites. Rylko's matrix decomposition is used for the higher-order contrast bounds to extend the obtained analytical bounds to piezoelectric fibrous composites. The supplementary materials contain the results of numerical-symbolic computations, the long analytical formulas for the effective constants and bounds up to O(f17), where f stands for concentration.