Variational‐based modeling of micro‐electro‐elasticity with electric field‐driven and stress‐driven domain evolutions
Variational‐based modeling of micro‐electro‐elasticity with electric field‐driven and stress‐driven domain evolutions
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基于电场驱动和应力驱动域演化的微电弹性建模
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Rosato
中科院分区：
文献类型：
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作者：
C. Miehé;Dominic Zäh;D. Rosato
最近，对具有机电耦合的所谓功能或智能材料的兴趣日益增加，例如铁电压电陶瓷。这些材料的特征在于微观结构特性，其可以通过外部应力和电场刺激而改变，因此可以用作传感器和致动器中的有源组件。机电耦合效应是由于具有均匀极化取向的微结构畴的存在和重排引起的。这些高度非线性和耗散机制，发生在微尺度上的铁电压电陶瓷的理解和有效的模拟，是当前研究的一个关键挑战。本文并没有为这些现象提供一个新的物理模型，而是提供了一种基于严格利用率型变分原理的新的数学建模方法。这提供了一个新的洞察力的结构的耦合问题，其中的控制场方程出现的欧拉方程的变分声明。我们概述了一个基于变分的微电弹性模型，用于描述铁电陶瓷中电和机械驱动电畴的微结构演化，该模型还包含了周围的自由空间。为此，我们将最近开发的多场增量变分原理从局部扩展到梯度扩展耗散响应，并通过Ginzburg-Landau型相场模型将其专门化，其中畴壁的厚度作为长度尺度进入公式。这作为一个典型的紧凑，对称的有限元实现的自然起点，考虑机械位移，微观极化，和极化引起的电位作为主要领域。后者被定义在固体域和周围的自由空间。数值模拟处理电场驱动和应力驱动加载过程的畴壁运动，包括电势向自由空间的扩展。版权所有© 2012约翰威利父子有限公司.
Recently, increasing interest in so‐called functional or smart materials with electromechanical coupling has been shown such as ferroelectric piezoceramics. These materials are characterized by microstructural properties, which can be changed by external stress and electric field stimuli, and hence find use as the active components in sensors and actuators. The electromechanical coupling effects result from the existence and rearrangement of microstructural domains with uniformly oriented electric polarization. The understanding and efficient simulation of these highly nonlinear and dissipative mechanisms, which occur on the microscale of ferroelectric piezoceramics, are a key challenge of the current research. This paper does not offer a substantially new physical model of these phenomena but a new mathematical modeling approach based on a rigorous exploitation of rate‐type variational principles. This provides a new insight in the structure of the coupled problem, where the governing field equations appear as the Euler equations of a variational statement. We outline a variational‐based micro‐electro‐elastic model for the microstructural evolution of both electrically and mechanically driven electric domains in ferroelectric ceramics, which also incorporates the surrounding free space. To this end, we extend recently developed multifield incremental variational principles of electromechanics from local to gradient‐extended dissipative response and specialize it by a Ginzburg–Landau‐type phase field model, where the thickness of the domain walls enters the formulation as a length scale. This serves as a natural starting point for a canonical compact, symmetric finite element implementation, considering the mechanical displacement, the microscopic polarization, and the electric potential induced by the polarization as the primary fields. The latter is defined on both the solid domain and a surrounding free space. Numerical simulations treat domain wall motions for electric field‐driven and stress‐driven loading processes, including the expansion of the electric potential into the free space. Copyright © 2012 John Wiley & Sons, Ltd.
耗散电磁力学的变分原理：功能材料宏观建模的框架
影响因子：
2.9
作者：
D. Rosato;B. Kiefer
通讯作者：
B. Kiefer