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.

在这项工作中，开发了一种 3D 半解析有限元法 (SAFEM) 来计算压电纤维增强复合材料 (PFRC) 的有效性能。在这里，计算是在单位单元的八分之一中实现的，以简化方法。据报道，对由在软非压电矩阵（聚合物）中具有方形和六边形空间排列的压电陶瓷单向纤维（PZT）制成的周期性 PFRC 的有效特性的预测作为验证 3D 方法的一种方式。当短纤维变成长纤维时，极限情况使我们能够与文献中报告的结果进行比较。为了分析作为纤维相对长度函数的有效特性，考虑两种情况：(i) 恒定体积分数和 (ii) 恒定纤维半径。恒定体积分数的情况特别令人感兴趣，因为根据 Voigt-Reuss-Hill 近似，有效性质应该保持不变。然后，为了分析这种情况，还显示了机械和电场。获得的结果显示出物理一致的行为。通过与渐近均匀化和代表性体积元方法进行比较，获得了良好的一致性。还实施了 3D SAFEM 以研究骨压电行为，注意矿化相对有效骨的作用。通过与渐近均匀化和代表性体积元方法进行比较，获得了良好的一致性。还实施了 3D SAFEM 以研究骨压电行为，注意矿化相对有效骨的作用。通过与渐近均匀化和代表性体积元方法进行比较，获得了良好的一致性。还实施了 3D SAFEM 以研究骨压电行为，注意矿化相对有效骨的作用。\(d_{333}^{*}\)压电系数。