Abstract An interaction of a tunnel conductive crack and a distant strip electrode situated at the interface between two piezoelectric semi-infinite spaces is studied. The bimaterial is subject by an in-plane electrical field parallel to the interface and by an anti-plane mechanical loading. Using the presentations of electromechanical quantities at the interface via sectionally-analytic functions the problem is reduced to a combined Dirichlet-Riemann boundary value problem. Solution of this problem is found in an analytical form excepting some one-dimensional integrals calculations. Closed form expressions for the stress, the electric field and their intensity factors, as well as for the crack faces displacement jump are derived. On the base of these presentations the energy release rate is also found. The obtained solution is compared with simple particular case of a single crack without electrode and the excellent agreement is found out. An auxiliary plane problem for open and closed cracks between two isotropic materials is also considered. The mathematical model of this problem is identical to the above one, therefore, the obtained solution is used for this model. It is compared with finite element solution of a similar problem and good agreement is found out.

中文翻译：

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两种压电材料界面处的导电裂纹和远程电极

摘要 研究了隧道导电裂纹与位于两个压电半无限空间界面处的远距离条状电极的相互作用。双材料受到平行于界面的面内电场和反面机械载荷的影响。使用通过截面解析函数在界面上表示的机电量，该问题被简化为组合 Dirichlet-Riemann 边值问题。除了一些一维积分计算外，该问题的解决方案可以通过解析形式找到。推导出应力、电场及其强度因子以及裂纹面位移跳跃的闭合形式表达式。在这些介绍的基础上，还发现了能量释放率。将所得解与无电极单裂纹的简单特例进行比较，发现了极好的一致性。还考虑了两种各向同性材料之间开裂和闭合裂纹的辅助平面问题。该问题的数学模型与上述相同，因此将得到的解用于该模型。将其与类似问题的有限元解法进行比较，发现吻合较好。