Based on the Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable triangle nano-hole in magnetoelectroelastic materials with surface effect is studied. The exact solutions of the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate are obtained under the boundary conditions of magnetoelectrically permeable and impermeable. The numerical examples show the influence of surface effect on the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate under two different boundary conditions. It can be seen that the surface effect leads to the coupling of stress, electric and magnetic field, and with the increase of cavity size, the influence of surface effect begins to decrease until it tends to classical elasticity theory.

中文翻译：

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磁电弹性材料中导磁正三角形纳米孔三个纳米裂纹的反平面断裂问题

基于Gurtin-Murdoch表面/界面模型和复势理论，通过构建新的共形映射，研究了具有表面效应的磁电弹性材料中磁电导三角形纳米孔中三个纳米裂纹的反平面断裂问题。 . 得到了磁电导磁和不导磁边界条件下应力强度因子、电位移强度因子、磁感应强度因子和能量释放率的精确解。数值算例显示了两种不同边界条件下表面效应对应力强度因子、电位移强度因子、磁感应强度因子和能量释放率的影响。