磁电弹性材料中含有带四条纳米裂纹的正4n边形纳米孔的反平面断裂问题  

Anti-plane fracture problem of four nano-cracks emanating from a regular 4n-polygon nano-hole in magnetoelectroelastic materials

作　　者：杨东升 刘官厅[1] Yang Dong-Sheng;Liu Guan-Ting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《物理学报》2020年第24期175-184,共10页Acta Physica Sinica

基　　金：国家重点研发计划(批准号:2017YFC1405605);自然资源部海洋遥测技术创新中心创新青年基金(批准号:21k20190088);内蒙古自然科学基金(批准号:2018MS01005);内蒙古师范大学研究生科研创新基金(批准号:CXJJS19098)资助的课题.

摘　　要：基于Gurtin-Murdoch表面理论和保角变换技术,研究了磁电弹性材料中含有带四条纳米裂纹的正4n形纳米孔的反平面断裂问题.得出了考虑表面效应时磁电非渗透边界条件下的应力强度因子、电位移强度子、磁感应强度因子和能量释放率的精确解.数值算例展示了表面效应和孔口尺寸对磁电非渗透边界条件应力强度因子、电位移强度因子、磁感应强度因子和能量释放率的影响.研究发现,考虑表面效应时的应场强度因子、电位移强度因子和磁感应强度因子具有明显的尺寸依赖,并且当孔口尺寸增加到一定程度表面效应的影响开始减小,最终趋于经典弹性理论.According to the conformal mapping from the exterior region of the regular n-polygon hole to the exterior region of a unit circle and from the exterior region of four cracks emanating from a circle to the interior region of a unit circle,a new conformal mapping is constructed to map the exterior region of four cracks emanating from a regular 4n-polygon hole to the interior of a unit circle.Then,based on the Gurtin-Murdoch surface/interface model and complex method,the anti-plane fracture of four nano-cracks emanating from a regular 4n-polygon nano-hole in magnetoelectroelastic material is studied.The exact solutions of stress intensity factor,electric displacement intensity factor,magnetic induction intensity factor,and energy release rate are obtained under the boundary condition of magnetoelectrically impermeable with considering the surface effect.Without considering the effect of the surface effect,the exact solution of four cracks emanating from a regular 4n-polygon hole in a magnetoelectroelastic material can be obtained.The numerical results show the influences of surface effect and the size of defect on the stress intensity factor,electric displacement intensity factor,magnetic induction intensity factor and energy release rate under the magnetoelectrically impermeable boundary condition.It can be seen that the stress intensity factor,electric displacement intensity factor,and magnetic induction intensity factor are significantly size-dependent when considering the surface effects of the nanoscale defects.And when the size of defect increases to a certain extent,the influence of surface effect begins to decrease and finally tends to follow the classical elasticity theory.When the distance between the center and the vertex of the regular 4n-polygon nano-hole is constant,the dimensionless field intensity factor decreases gradually with the increase of the number of edges,and approaches to the conclusion of a circular hole with four cracks.With the increase of the relative size of the crack,the dimensionless

关 键 词：磁电弹性材料 表面效应 纳米尺度 

分 类 号：TB383.1[一般工业技术—材料科学与工程] O346.1[理学—固体力学]