Abstract This work introduces a set of analytical expressions that simplifies the procedure of obtaining closed-form formulas to estimate the effective piezoelectric properties of polycrystalline aggregates formed by crystals of all the 21 non-centrosymmetrical classes and with arbitrary textures. The expressions are derived from orientational averages of third-order piezoelectric tensors of the individual crystals that are weighted by orientational distribution functions. The averaging is done by using generalized spherical harmonic series expansions. Improvements with respect to previous works in the literature are twofold: all crystal symmetries are considered and no symmetry restrictions are imposed to texture. The versatility of the introduced expressions is demonstrated on an example of BaTiO3 polycrystals with uniaxial and biaxial textures characterized by single and double Gaussian distributions, respectively. The results for uniaxial texture are in perfect agreement with the results published in the literature. The biaxial texture is discussed in detail and analyzed for a set of limiting cases.

中文翻译：

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用于估计任何晶体对称性的织构多晶的有效压电张量的解析表达式

摘要 这项工作引入了一组解析表达式，简化了获得闭式公式的过程，以估计由所有 21 种非中心对称类和任意纹理的晶体形成的多晶聚集体的有效压电特性。这些表达式来自于由取向分布函数加权的单个晶体的三阶压电张量的取向平均值。平均是通过使用广义球谐级数展开来完成的。相对于文献中以前的工作的改进是双重的：考虑了所有晶体对称性，并且没有对纹理施加对称性限制。所引入表达式的多功能性在一个具有单轴和双轴织构的 BaTiO3 多晶实例上得到了证明，该实例分别具有单高斯分布和双高斯分布特征。单轴织构的结果与文献中发表的结果完全一致。详细讨论了双轴纹理，并针对一组极限情况进行了分析。