在裂纹尖端引入奇异单元的偶应力有限元法

Couple stress finite element method using singular element at crack tip

针对在微观状态下结构力学行为会受尺度效应影响的问题,在偶应力理论中考虑微观结构的旋转梯度可以较好解释结构的尺度效应.建立基于一般偶应力理论的有限元法的基本方程,并在裂纹尖端引入奇异单元,计算受单向拉伸的中心斜裂纹板裂纹尖端场的应力强度因子(Stress Intensity Factor,SIF),分析特征长度变化对SIF的影响,对比偶应力理论下的结果与经典理论下的结果.结果表明:在裂纹尖端引入奇异单元可以提高计算精度和稳定性;偶应力使得裂纹尖端SIF比经典理论下的值小,并且SIF随着特征长度增大而减小.

As to the issue that the mechanical behavior of micro-structure may be affected by the scale effect, the couple stress theory can explain the scale effect very well by considering the effect of rotating gradient. The basic equation of finite element method is built based on the general couple stress theory and the singular element is introduced into crack tip. The Stress Intensity Factor（SIF） of the crack tip field of a plate with incline center crack in uniaxial tension is calculated, and the effect of characteristic length on the SIF is analyzed; the results obtained by the couple stress theory and the classical theory are compared. The results show that, the calculation accuracy and stability can be improved by introducing singular element into crack tip, the SIF obtained by couple stress is less than that determined by the classical theory, and the SIF increases with the decrease of the value of characteristic length.