Dynamic and static analysis for two semi-infinite cracks in finite magnetoelectroelastic strip
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摘要: 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。Abstract: The crack in strip is often used in fracture mechanics as research model. There is a magnetoelectroelastic elastomer which contains infinite collinear cracks, when crack surface on the left side near crack tip is under the electromagnetic force load and anti-plane shear stress along the crack surface, elastomer tends to produce dynamic fracture. By using arch transform formula of complex variable function method, the analytic solutions of the dynamic stress intensity factors and the mechanical strain energy release rate were presented with the boundary conditions that the surface of the crack was electrically and magnetically impermeable. When the movement velocity tends to zero, the analytic solutions is degraded to stationary state solution. Through numerical example, the fracture mechanism was analyzed, the influence of the geometry size of strip and crack, external force, electric field and magnetic field on energy release rate respectively under static state were discussed to help the design and manufacture of related devices.
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