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狭长体中的裂纹是断裂力学中经常采用的研究模型。含有共线无限长裂纹的条形磁电弹性体,当面内的力电磁和反平面的剪应力作用在左边裂纹尖端附近的一段裂纹面上时,往往会产生动态断裂。利用复变函数法中的拱形变换公式,导出了磁电全非渗透型边界条件下左裂纹尖端动态的应力强度因子以及机械应变能释放率的解析解。当运动速度趋于零时退化为静止状态下的解。通过数值算例分析了断裂机理,讨论了静止状态下狭长体和裂纹的几何尺寸、外力、电场和磁场分别对能量释放率的影响,为相关器件的设计与制造提供了帮助。
The crack in the narrow body is a frequently used research model in fracture mechanics. Bar-shaped magnetoelastic elastomers containing co-linear infinite cracks tend to produce dynamic fractures when the in-plane force electromagnetic and anti-plane shear stresses act on the first crack surface near the left crack tip. The dynamic stress intensity factor of the left crack tip and the analytical solution of the mechanical strain energy release rate are deduced by using the arc transformation formula in the complex function method. When the speed of motion tends to zero, it degenerates into a solution at rest. The fracture mechanism is analyzed by numerical examples. The geometrical dimensions of the slender body and crack under static state, the influence of external force, electric field and magnetic field on the energy release rate are discussed respectively, which is helpful for the design and manufacture of related devices.