Analysis of Mode Ⅲ Interface Fracture for Magneto-Electro-Elastic Materials

电磁弹性材料Ⅲ型界面断裂分析

¹ State Key Laboratory of Structure Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China
² School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China

Received: 25 December 2017

Abstract

A novel finite element discretized symplectic method is developed for analyzing interface fracture of magneto-electro-elastic (MEE) materials under anti-plane loads. The overall cracked body is meshed by conventional finite elements and divided into a finite size singular region near the crack tip (near field) and a regular region far away from the crack tip (far field). In the near field, a based-Hamiltonian model is introduced to find the analytical series expressions, and the large number nodal unknowns are condensed into a small set of the undetermined coefficients of the symplectic series by a transformation. The nodal unknowns in the far field remain unchanged. The stress, electric and magnetic intensity factors, energy release rates (ERRs) and explicit expressions of singular field variables in the near field are simultaneously obtained without any processing.

摘要

针对电磁弹性复合材料的界面断裂问题，提出一种全新的辛离散有限元方法。该方法在传统有限元网格划分的基础上，将整体结构进一步划分并为2类区域，即包含裂纹尖端的近场奇异区和不包含裂纹尖端的远场非奇异区。在近场区域内建立哈密顿求解体系，通过引入解析的辛本征解函数，将该区域内大量的节点未知量转化为少量辛本征解的待定系数。远场区域内的节点未知量保持不变。该方法无需后处理程序，应力场、电场、磁场强度因子、能量释放率以及近场区域内奇异物理量的显式表达式可以同时获得。