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Numerical Convergence Study of Heterogeneous Multi-scale Method Piezoelectric Composites

机译：非均相多尺度压电复合材料的数值收敛研究

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摘要

In this paper, we focus on multi -- scale modeling and simulation of piezo electric composite materials, Piezo electricity is the ability of some materials to generate an electric field or electric potential in response to applied mechanical stress.And it isreversible in piezoelectric materials.This property can be reflected in the constitutive relations as coupling of mechanical field and electrical field. First, for those materials with periodic microstructure, we deduced the macroscopic model from the microscopic model of piezoelectric composite material and carried out the corresponding convergence analysis under the flame of homogenization. Second, for general cases, we also designed the multi-scale model under the frame of HMM and gave out error estimate between the HMM solutions and the homogenization solutions.Finally we give out numerical examples.The macroscopic models of type 1-3 piezoelectric coinpositematerials are got by the two methods mentioned above. Also, we gi ve out the comparison and discussion about the numerical results we get in the numerical examples.
机译：在本文中，我们专注于压电复合材料的多尺度建模和仿真，压电是某些材料响应施加的机械应力而产生电场或电势的能力，并且在压电材料中是可逆的。该性质可以在本构关系中反映为机械场和电场的耦合。首先，对于具有周期性微观结构的材料，我们从压电复合材料的微观模型中推导了宏观模型，并在均质化的火焰下进行了相应的收敛性分析。其次，对于一般情况，我们还在HMM框架下设计了多尺度模型，并给出了HMM解和均化解之间的误差估计，最后给出了数值示例.1-3型压电复合材料的宏观模型是通过上述两种方法获得的。另外，我们对数值示例中得到的数值结果进行了比较和讨论。

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