An extended dielectric crack model is proposed to capture the effects of the physical properties of crack interior on crack-tip thermoelectroelastic fields. The typical crack-face boundary conditions can be retrieved by considering the limiting cases of electrical permeability and thermal conductivity inside a crack. Making use of the Fourier transform technique, the problem of a thermopiezoelectric strip weakened by a Griffith crack is investigated and transformed to solve the system of the second kind Fredholm integral equations with Cauchy kernel. The Lobatto–Chebyshev collocation method is used to form a nonlinear system of algebraic equations, which is solved by elaborating on an algorithm. The crack-tip thermoelectroelastic fields are determined by using the approximate solutions. Numerical simulations are carried out to show the variations of the fracture parameters of concern under applied thermoelectromechanical loads, the physical properties of the dielectric medium inside the crack and the geometry of the cracked thermopiezoelectric strip. Some comparisons with the experimental results are reported to reveal the effectiveness of the extended dielectric crack model.

中文翻译：

---

热压电带断裂分析的扩展介电裂纹模型

提出了扩展的介电裂纹模型，以捕获裂纹内部的物理性质对裂纹尖端热电弹性场的影响。可以通过考虑裂纹内部的电导率和导热率的极限情况来检索典型的裂纹面边界条件。利用傅里叶变换技术，研究了由格里菲斯裂纹削弱的热压电带问题，并进行了变换，以解决带有柯西核的第二类Fredholm积分方程组。Lobatto-Chebyshev搭配方法用于形成代数方程组的非线性系统，通过详细阐述算法来解决。裂纹尖端的热电弹性场是使用近似解确定的。进行了数值模拟，以显示在施加的热电机械载荷下所关注的断裂参数的变化，裂纹内部的介电介质的物理性质以及裂纹的热压电体的几何形状。据报道，与实验结果的一些比较揭示了扩展介电裂纹模型的有效性。