Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites based on effective medium theory

Explicit formulas were derived for the effective piezoelectric stress coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix which were then combined to give the more commonly used strain coefficients. Comparisons with other predictions, including the predictions given by numerically solving the EMT scheme, were also made and it was observed that the analytic and numeric EMT schemes agreed with each other very well for an inclusion of volume fraction not exceeding 60%.