压电材料中椭圆形夹杂附近的应力场

Stress Field Near to an Elliptic Inclusion in a Piezoelectric Medium

摘要: 压电材料在传感器件等多个领域有着广泛的用途。由于压电陶瓷材料非常脆，因而其应力集中部位的应力场分布问题受到了广泛关注。本文采用Stroh公式法、解析连续方法、保角变换法和叠加法得到了任意远场均匀热电弹性载荷作用下，椭圆形各向异性压电体内嵌于无限大各向异性压电基体中的解析解。以复矩阵的形式给出了基体和夹杂中的温度场和应力函数的解。结果表明应力载荷和电载荷将导致夹杂体中常应力场的出现，而温度载荷将导致线性应力场的出现。与一些相关工作的比较表明本文的解是正确的和普遍的。

Abstract: Piezoelectric material can be used in piezoelectric sensors and other fields. The problem of its stress field distribution in the zone of stress concentration has received widespread attention due to its brittleness. This paper pre- sents an analytical solution for an elliptical anisotropic piezoelectric inclusion embedded in an infinite anisotropic pie- zoelectric matrix subjected to arbitrary far-field uniform loadings by employing the Stroh formalism, the method of analytical continuation, the technique of conformal mapping, and the concept of superposition. Solutions of the tem- perature and stress functions either in the matrix or in the inclusion are expressed in complex matrix notation. It shows that mechanic loading and electric loading lead to the appearance of the constant stress fields in the inclusion and heat flux only leads to that of the linear stress fields. Comparison with some related works shows that the present solutions are valid and general.