Semi-analytic finite element method applied to short-fiber-reinforced piezoelectric composites

In this work, a 3D semi-analytical finite element method (SAFEM) is developed to calculate the effective properties of piezoelectric fiber-reinforced composites (PFRC). Here, the calculations are implemented in one-eighth of the unit cell to simplify the method. The prediction of the effective properties for periodic PFRC made of piezoceramic unidirectional fibers (PZT) with square and hexagonal space arrangements in a soft non-piezoelectric matrix (polymer) is reported as a way to validate the 3D approach. The limit case, when short fibers become long ones, allows us to compare with results reported in the literature. For the analysis of effective properties as a function of fiber relative length, two cases are considered: (i) constant volume fraction and (ii) constant fiber radius. The constant volume fraction case is of special interest because according to the Voigt–Reuss–Hill approximation, the effective properties should remain constant. Then, in order to analyze this case, mechanical and electric fields are also shown. The obtained results show a physically congruent behavior. Good coincidences are obtained by comparing with asymptotic homogenization and the representative volume element methods. The 3D SAFEM is also implemented to study the bone piezoelectric behavior with attention to the role of the mineralized phase on the effective $$d_{333}^{*}$$ piezoelectric coefficient.