Finite element analyses of cracks in piezoelectric structures: a survey
Finite element analyses of cracks in piezoelectric structures: a survey
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DOI：
10.1007/s00419-006-0059-z
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发表时间：
2006-08
影响因子：
2.8
通讯作者：
M. Kuna
中科院分区：
文献类型：
--
作者：
M. Kuna
压电材料在机电一体化、智能结构或微系统技术等现代技术领域有着广泛的应用，在这些领域中它们充当传感器或执行器。对于电-机械联合载荷作用下压电结构的强度和可靠性评估，裂纹缺陷的存在起着重要的作用。同时，压电断裂力学已经建立得相当成熟，但要将其应用于实际的压电结构中的裂纹形态和载荷情况，则需要使用有限元或边界元等数值方法。本文综述了静载和动载作用下二维和三维压电结构裂纹机电耦合边值问题的有限元计算方法的研究现状。为了非常准确和有效地计算相关的断裂参数，数值处理必须考虑裂纹尖端的机械场和电场的奇异性。文中详细介绍了(1)特殊的奇异裂纹尖端单元，(2)由近端场确定强度因子KI-KIV，(3)修正的裂纹闭合积分，(4)机电J积分的计算，以及(5)相互作用积分的利用。特别强调了裂纹内部介质的真实建模，从而导致特定的电裂纹面边界条件。这些技术的准确性、效率和适用性通过各种实例问题进行了检验，并讨论了它们在实际应用中的优点和缺点。
Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, smart structures or microsystem technology, where they serve as sensors or actuators. For the assessment of strength and reliability of piezoelectric structures under combined electrical and mechanical loading, the existence of cracklike defects plays an important role. Meanwhile, piezoelectric fracture mechanics has been established quite well, but its application to realistic crack configurations and loading situations in piezoelectric structures requires the use of numerical techniques as finite element methods (FEM) or boundary element methods (BEM). The aim of this paper is to review the state of the art of FEM to compute the coupled electromechanical boundary value problem of cracks in 2D and 3D piezoelectric structures under static and dynamic loading. In order to calculate the relevant fracture parameters very precisely and efficiently, the numerical treatment must account for the singularity of the mechanical and electrical fields at crack tips. The following specialized techniques are presented in detail (1) special singular crack tip elements, (2) determination of intensity factorsKI–KIVfrom near tip fields, (3) modified crack closure integral, (4) computation of the electromechanicalJ-integral, and (5) exploitation of interaction integrals. Special emphasis is devoted to a realistic modeling of the dielectric medium inside the crack, leading to specific electric crack face boundary conditions. The accuracy, efficiency, and applicability of these techniques are examined by various example problems and discussed with respect to their advantages and drawbacks for practical applications.