We consider the linear thermo-piezoelectric properties of a ceramic matrix with cylindrical empty pores distributed periodically. The asymptotic homogenization method is applied to an elliptical tensor-weighted boundary value problem in the Stress-Charge-Entropy formulation of the constitutive relations with rapidly oscillating coefficients and free boundary conditions on the surfaces of the pores. For different shapes of the pore cross section, we solve the local problems via finite element method to compute the effective coefficients as functions of the physical properties of the matrix, the shape of the pore cross section and their volume fraction. The numerical results show excellent agreement with analytical formulae. When the effective coefficients are transformed to the Strain-Charge-Entropy formulation of the constitutive relations, they become independent of the shape of the cross section, which further validates the importance of the analytical formulae. We compute the piezoelectric and pyroelectric figures of merit for energy-harvesting applications, which depend on the effective coefficients and are compared with recent experimental results. This contribution could be useful for fine-tuning the properties of this class of materials for energy-harvesting applications.

中文翻译：

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通过渐近均匀化和有限元方法计算多孔陶瓷有效热压电性能，以进行能量收集

我们考虑具有周期性分布的圆柱形空孔的陶瓷基体的线性热压电性能。渐近均质化方法应用于本构关系的应力-电荷-熵公式中的椭圆张量加权边界值问题，该本构关系具有快速振荡的系数和孔表面的自由边界条件。对于不同形状的孔横截面，我们通过有限元方法解决了局部问题，以计算有效系数作为基质物理性质，孔横截面形状及其体积分数的函数。数值结果与解析公式吻合良好。当有效系数转换为本构关系的应变-电荷-熵公式时，它们变得与横截面的形状无关，这进一步证实了分析公式的重要性。我们计算了能量收集应用的压电和热电性能，这取决于有效系数，并与最近的实验结果进行了比较。这种贡献可能有助于微调此类材料在能量收集应用中的性能。