考虑界面应力时周期材料宏细观电弹性能的解析方法研究

项目名称： 考虑界面应力时周期材料宏细观电弹性能的解析方法研究

项目编号： No.11302186

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 肖俊华

作者单位： 燕山大学

项目金额： 23万元

中文摘要： 周期非均匀材料由于微结构和边界条件的特殊性，给力学工作者获得其有效的解法并应用于复合智能材料带来困难。当夹杂的尺寸在纳米量级时，非均匀材料的界面效应变得非常明显。本项目基于Gurtin-Murdoch界面理论和解析函数边值问题理论，研究力电载荷作用下考虑夹杂界面应力时周期材料的细观电弹场(应力应变场、电位移场和电场)和宏观电弹性能(弹性模量、压电模量和介电模量)。从该类非均匀材料的细观力学模型出发，建立力电耦合作用时周期纳米材料的物理力学表征，提出所研究问题的边值问题并寻求其有效的解析方法，揭示夹杂的微结构特征(截面形状、材料参数、分布方式、体积分数和界面性能等)对周期纳米材料的细观局部场和宏观有效性能的关联。本项目以期为力电载荷作用下周期纳米材料宏细观电弹性能的有效分方法的发展作出新成果，为力学和材料科学家设计与研制复合智能材料提供适用范围广、计算效率和精度高的细观力学分析方法。

中文关键词： 界面效应；电弹性能；广义自洽法；宏观有效性能；细观场

英文摘要： Due to the particularity of microstructure and boundary conditions for the periodic heterogeneous materials, it is difficulty to obtain the effective solution applying in smart composites. Interface effects become prominent when the size of the inhomogeneity is on the order of nanometer. By applying the theory of Gurtin-Murdoch interface model and boundary Value theory of analytic functions, the microscopic electro-elastic fields(stress and strain fields, electric displacement field, electric field) and macroscopic electro-elastic properties(the elastic, dielectric and piezoelectric moduli) for periodic heterogeneous materials with interface stress subjected to mechanical-electric loads will be investigated. In this research project, multi-field coupling physical and mechanical characterization will be established from the micromechanics model of such heterogeneous materials, and the rigorous effective solution will be presented for the considering boundary problem. Then the focus will be put on the revelation of the microscopic local fields and macroscopic effective electroelastic moduli of such periodic nano heterogeneous materials with the microstructures properties (section shape, material parameter, distribution pattern, volume fraction and interfacial property) of the inhomogeneity. The research project wi

英文关键词： Interface effect；Electro-elastic properties；Generalized self-consistent method；Macroscopic effective property；Microscopic field