压电穿孔结构的两尺度均匀化
Two-scale homogenization of piezoelectric perforated structures
AI总结：
针对周期性穿孔压电体中的弹性-电耦合方程，采用两尺度收敛方法推导出均匀化系统，并验证了渐近展开的前两项。
摘要：
我们关注具有快速振荡系数的弹性-电耦合方程在周期性穿孔压电体中的均匀化问题。我们验证了问题解通常渐近展开中的前两项。对于本文的主要收敛结果，我们使用了{\it 两尺度收敛}的概念。周期问题的极限得到了一个两尺度均匀化系统。在静态极限下，该方法提供的均匀化电弹性系数与其他均匀化技术（渐近均匀化、$\Gamma$-收敛）推导出的系数一致。
英文摘要：
We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of {\it two-scale convergence}. A two-scale homogenized system is obtained as the limit of the periodic problem. While in the static limit the method provides homogenized electroelastic coefficients whicht coincide with those deduced from other homogenization techniques (asymptotic homogenization, $Γ$-convergence).
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