Indentation of the coated piezoelectric transversely isotropic half-space by a conical conductive punch is modeled. The coating is assumed to be functionally-graded (continuously inhomogeneous in depth) with all group of electromechanical properties varying independently in depth according to arbitrary continuous functions or piecewise homogeneous. The problem is described mathematically in terms of linear electroelasticity and reduced to solution of a system of dual integral equations using the Hankel’s integral transformations. Closed-form approximated analytical solution of this system is obtained using the bilateral asymptotic method taking into account asymptotic properties of the kernel transforms. Expressions for the contact pressure, electric induction are obtained in an analytical form suitable for engineering analysis as well as the relations for the indentation force, total electric charge, indentation depth, contact radius and electric potential. Analytical form of results clearly demonstrates the contribution of mechanical and electric loading to the total solution and influence of the coating’s thickness and its properties on contact characteristics. Numerical results for homogeneous and two types of functionally-graded coatings illustrate features of the theoretical results in a wide range of values of relative coatings thickness.

中文翻译：

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锥形导电冲头对压电 FGM 涂层半空间的压痕：近似解析解


模拟了锥形导电冲头对涂层压电横向各向同性半空间的压痕。假设涂层是功能分级的（深度连续不均匀），所有组机电性能根据任意连续函数在深度上独立变化或分段均匀。该问题用线性电弹性在数学上进行了描述，并简化为使用 Hankel 积分变换的对偶积分方程组的解。该系统的闭式近似解析解是使用双边渐近法获得的，同时考虑了核变换的渐近特性。接触压力、电感应的表达式以适合工程分析的解析形式获得，以及压痕力、总电荷、压痕深度、接触半径和电势的关系。结果的分析形式清楚地表明了机械和电气负载对总溶解的影响以及涂层厚度及其特性对接触特性的影响。均质涂层和两种类型的功能梯度涂层的数值结果说明了相对涂层厚度的广泛范围内的理论结果的特征。