磁电弹材料反平面切口奇性数值分析

磁电弹复合材料具有压电压磁的特点而被用于制作传感器等智能元件,在这些元器件中经常遇到界面端或切口问题,切口处由于易产生较高的奇异场而导致机械失效或电介击穿致使器件失效.本文主要研究磁电弹材料反平面切口的奇性问题.基于切口根部物理场的渐近展开假设,从应力平衡方程和电磁麦克斯韦方程组出发,导出了关于磁电弹材料反平面切口奇性指数的特征微分方程组,并将切口的力电磁学边界条件以及粘接材料的界面协调条件表达为奇性指数和特征角函数的组合.磁电弹材料切口反平面奇性指数的计算被转化为相应边界条件下常微分方程组特征值的求解问题,通过插值矩阵法计算出各阶奇性指数和相应的特征角函数.计算结果能提供减小切口奇性程度的切口角度和材料组合方案,更好地指导磁电弹智能元器件的结构设计.

Numerical analysis of the singularities for a magneto-electro- elastic notch under anti-plane deformation

Due to the capability of the conversion between mechanical, electric and magnetic energy, magneto-electro-elastic （MEE） materials can be applied to design sensors, actuators and other smart products. The notch and interfacial edge problem can always be encountered in these products. The singularity phenomenon is that the stress, electric displacement and magnetic induction may become theoretical infinite due to the materials or geometrical discontinuities at the vertex of notch. In practices, the mechanical failure or dielectric breakdown may initiate from the notch apex due to this high singularity. The present paper is trying to establish a new method to study the singularity at the vertex of notch encountered in MEE structures. Basing on the asymptotic assumption for the physical field near the notch tip, the singularities for a MEE notch under anti-plane deformation are investigated by the eigenfunction expansion approach. The characteristic differential equations respects to the singularities of the MEE notch are built from the equilibrium equations and Maxell equations. At the same time, the mechanical and electric boundary conditions together with the interfacial continuous conditions are expressed by the combination of the singularity orders and characteristic angle functions. Thus, the evaluation of the notch singularity orders is transformed into the problem of solving the ordinary differential equations under the designated boundary conditions. The singularity orders and the corresponding characteristic angle functions can be achieved by applying the interpolate matrix method to solve the obtained characteristic differential equations. The achieved results can provide the guidelines for the selection of notch angles and materials to reduce the singularity for the structure design of MEE products.