磁电弹性材料含纳米尺度唇口次生两不对称裂纹的反平面问题  

An Antiplane Problem of Magnetoelectroelastic Materials With Nanoscale Lip-Shaped Orifice With 2 Asymmetric Cracks

作　　者：姜丽娟[1,2] 刘官厅 高媛媛[1] 王程颜 郭怀民 JIANG Lijuan;LIU Guanting;GAO Yuanyuan;WANG Ghengyan;GUO Huaimin(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,P.R.China;College of Educational Science,Baotou Teacher’s College,Baotou,Inner Mongolia 014030,P.R.China;Center for Applied Mathematics Inner Mongolia,Hohhot 010022,P.R.China;College of Mathematics Science,Baotou Teacher’s College,Baotou,Inner Mongolia 014030,P.R.China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]包头师范学院教育科学学院,内蒙古包头014030 [3]内蒙古自治区应用数学中心,呼和浩特010022 [4]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《应用数学和力学》2024年第10期1332-1344,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12162027);内蒙古自然科学基金重点项目(2024ZD21);内蒙古自治区高等学校科学技术研究自然科学重点项目(NJZZ22574);内蒙古自然科学基金(2023LHMS01017);内蒙古自治区高等学校科学技术研究自然科学一般项目(NJZY23089)。

摘　　要：基于Gurtin-Murdoch表面弹性理论和磁电弹性(MEE)理论,利用解析函数的保角映射技术,研究了反平面机械载荷和面内电磁载荷作用下,MEE材料中含有纳米尺度唇口次生两不对称裂纹的断裂行为,给出了缺陷(裂纹和唇口孔)周围广义MEE应力场和裂纹尖端MEE场强度因子以及能量释放率的解析解.在特殊条件下,所得结果退化为已有结果或者给出新的结果.数值算例揭示了缺陷表面效应对裂纹尖端MEE场强度因子的影响与纳米圆孔半径、唇口孔的大小、唇口次生裂纹大小,以及外加的机-电-磁载荷有关,也揭示了考虑表面效应时,无量纲能量释放率随唇口宽度、无穷远处机械载荷、电载荷和磁载荷的变化而变化.Based on the Gurtin-Murdoch surface elasticity theory and the magnetoelectroelasticity(MEE)theory,the fracture behaviors of MEE materials containing nanoscale lip-shaped orifice with 2 asymmetric cracks under anti-plane mechanical loads and in-plane electromagnetic loads were investigated with the analytic function conformal mapping technique.Analytical solutions for the generalized MEE stress fields around defects(the lip-shaped orifice and cracks),as well as the crack tip MEE intensity factors and energy release rates,were given.Under special conditions,the obtained results would degenerate into existing results or offer new insights.Numerical examples reveal that,the defect surface effects on the MEE intensity factors are dependent on the radii of nano-sized circular holes,the size of the lip-shaped orifice,the size of secondary cracks originating from the lip-shaped orifice,and the applied MEE loads.Under the surface effect,the dimensionless energy release rate varies with the lip width,the infinity mechanical load,the infinity electrical load and the infinity magnetic load.

关 键 词：磁电弹性材料 表面效应 唇口次生两不对称裂纹 场强度因子 能量释放率 

分 类 号：O346.1[理学—固体力学]