中文摘要：

压电材料在传感器和半导体材料等领域的应用越来越普遍。运用均匀化和渐近展开分析方法,对具有小周期孔洞结构区域中的压电耦合问题分析了均匀化力学、介电常数的正则性。在理论研究中为对应材料的等效力学常数计算提供了理论依据,刻画了压电材料的等效物理行为,并对进一步得到高精度的数值模拟提供了算法依据。

英文摘要：

Piezoelectric composite materials have been widely used in sensors and semiconductor materials fields. Based on the two-scale method and homogenization method, the regularity of mechanic and electric homogenization constants were analyzed for piezoelectric composites in small periodic perforated domain. In theoretic research, the result could be taken as the scientific basis, and in numerical simulation the result could be applied to construct the high effective numerical solutions for these problems.