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首页> 外文会议>Conference on Smart Structures and Materials 2000 Active Materials: Behavior and Mechanics 6-9 March 2000 Newport Beach, USA >On a Non-Linear Finite Element Method for Piezoelectric Structures Made of Hysteretic Ferroelectric Ceramics
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On a Non-Linear Finite Element Method for Piezoelectric Structures Made of Hysteretic Ferroelectric Ceramics

机译：迟滞铁电陶瓷压电结构的非线性有限元方法

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摘要

A simple macroscopic constitutive law for ferroelectric and ferroelastic hysteresis effects of piezocermaics is presented. After summarizing the uniaxial formulation, it is generalized to a three dimensional tensorial formulation. This constitutive model has been implemented in the public domain finite elmeent code PSU of Stuttgart University (Germany). The fully coupled electro-mechanical boundary value problem for our hysteresis model is solved by incrementation of the loading history. In order to verify the capabilities of our tool, a multilayer like actuator geoemtry is analysed. It is shown that the remanent polarization remaining after poling gives rise to a non-vanishing distribution of the electric potential even if the voltage is reduced to zero at all electrodes. Concerning the residual stresses present after poling, a tnesile stress field perpendicular to the direction of the electrodes can be found in the passive region of the actuator where so-called poling cracks are known to occur. It is the key feature of our finite element tool that it allows to consider in structural mechanical analyses such phenomena as they are induced by the remanent hysteresis properties of piezocermaics.
机译：提出了压电陶瓷的铁电和铁弹性磁滞效应的简单宏观本构定律。总结了单轴公式后，将其概括为三维张量公式。本构模型已在德国斯图加特大学的公共领域有限元代码PSU中实现。通过增加加载历史可以解决我们的磁滞模型的完全耦合的机电边界值问题。为了验证我们工具的功能，对执行器几何体等多层材料进行了分析。可以看出，即使在所有电极上的电压都减小到零，极化之后剩余的剩余极化也会导致电势的分布消失。关于极化之后存在的残余应力，可以在致动器的无源区域中发现垂直于电极方向的张应力场，在该处已知发生所谓的极化裂纹。这是我们有限元工具的关键特征，它允许在结构力学分析中考虑由压电陶瓷的剩余磁滞特性引起的现象。

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