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通过构造新的保角映射,利用复变函数的方法,研究了含光滑顶点的正三角形孔边裂纹的横观各向同性的压电弹性体的反平面问题。在电可穿透和电不可穿透裂纹、孔周及裂纹面为自由表面的假设下,充分利用Cauchy积分公式和复变函数方法,得到了裂纹尖端的场强度因子和能量释放率的表达式。数值算例显示了在不同边界条件下裂纹的几何尺寸、机电载荷对能量释放率和机械应变能释放率的影响规律。结果表明:在电可通和电不可通边界条件下,裂纹长度和三角形边长的增加会导致能量释放率增加,机械载荷则总是促进裂纹的扩展。在电不可通边界条件下电位移可以促进或抑制裂纹的扩展,而在电可通边界条件下电位移对裂纹扩展没有影响。
By constructing a new conformal mapping and using the method of complex functions, the anti-plane problem of transversely isotropic piezoelectric elastomers with a smooth triangular triangular hole edge crack is studied. Under the assumption that the electricity can penetrate through and the electricity can not penetrate the crack, the hole circumference and the crack surface are free surfaces, the Cauchy integral formula and the complex function method are fully used to obtain the expression of the field strength factor and the energy release rate at the crack tip . The numerical examples show the crack size, the influence of electromechanical load on the energy release rate and the mechanical strain energy release rate under different boundary conditions. The results show that the increase of the crack length and the length of the triangular side leads to the increase of the energy release rate, while the mechanical load always promotes the crack propagation. Electric displacement can promote or suppress the crack propagation under the electrically non-boundary conditions, while the electric displacement does not affect the crack propagation under the condition of electrically conductive boundary.