弹性电介质复合材料的多极材料力学

周树昂

弹性电介质复合材料的多极材料力学

周树昂

斯德哥尔摩皇家工学院力学系瑞典

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出版历程
- 收稿日期: 1988-04-19
- 刊出日期: 1990-03-15

Material Multipole Mechanics of Elastic Dielectric Composites

Zhou Shu-ang

Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden

摘要

摘要: 本文根据物质材料的多极概念研究了弹性电介质复合材料的宏观力学和电的性质.特别是:运用多极物质材料的统计连续体理论,可以得到不均匀颗粒间的电弹性相互作用和微结构(尺寸、形状、取向…)对复合材料的宏观性质的影响.本文首先给出了在某一无限的弹性电介质体中具有电极化的椭球的弹性不均匀性的基本解,这个解是由于电弹性相互作用而对Eshelby的经典弹性解的修正.其次,本文导出了电弹性相互作用的弹性电介质复合材料的宏观本构关系和宏观材料参量,最后对稀释的复合材料的具有统计的异向性的、形状效应的、以及电弹相互作用的一些问题进行了定量计算.

Abstract: The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

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