中文摘要：

在压电的材料的裂缝问题的现在的调查基于非局部的理论被执行。在一些操作以后，透不过的裂缝，可渗透的裂缝(裂缝差距充满 NaCI 答案)，并且半渗透的裂缝(裂缝差距充满空气或硅油)被在裂缝表面上假定正常电的排水量是一个未知变量归结为一致明确的表达。因此，有未知正常电的排水量的一个三倍的不可分的方程被建立。由使用牛顿反复的方法并且解决三倍的不可分的方程，裂缝表面上的正常电的排水量不再是相当，由以前的研究决定它取决于遥远的联合机电的装载的一个常数，这被发现。压力和电的排水量领域的数字结果证明在裂缝尖端没有奇特以便压力仍然保持有限。是大意义裂缝表面上的具体电的边界条件对近尖端的领域施加重要影响并且这样在在非局部的压电的材料评估裂缝稳定性起一个重要作用。更明确地，透不过的裂缝模型总是在裂缝尖端过高估计有限压力，而可渗透的裂缝模型总是低估他们。

英文摘要：

The present investigation of the crack problem in piezoelectric materials is performed based on the non-local theory. After some manipulations, the impermeable crack, the permeable crack （the crack gap is full of NaCI solution）, and the semi-permeable crack （the crack gap is full of air or silicon oil） are reduced to a uniform formulation by assuming the normal electric displacement on the crack surfaces to be an unknown variable. Thus, a triple integral equation with the unknown normal electric displacement is established. By using the Newton iterative method and solving the triple integral equation, it is found that the normal electric displacement on the crack surfaces is no longer a constant as determined by previous studies, rather, it depends upon the remote combined electromechanical loadings. Numerical results of the stresses and electric displacement fields show that there are no singularities at the crack tips so that the stresses remain finite. It is of great significance that the concrete electric boundary condition on the crack surfaces exerts significant influence on the near-tip fields and in this way plays an important role in evaluating the crack stability in the non-local piezoelectric materials. More specifically, the impermeable crack model always overestimates the finite stresses at the crack tips, whereas the permeable crack model always underestimates them.