A nonlinear field theory of deformable dielectrics
A nonlinear field theory of deformable dielectrics
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DOI：
10.1016/j.jmps.2007.05.021
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发表时间：
2008-02
影响因子：
5.3
通讯作者：
Z. Suo;Xuanhe Zhao;W. H. Greene
中科院分区：
文献类型：
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作者：
Z. Suo;Xuanhe Zhao;W. H. Greene
两个难题长期以来一直困扰着介电固体场论。首先，当两个电荷置于介电固体内时，它们之间的力是不可测量的。其次，当介电固体变形时，真实电场和真实电位移不是功共轭。本文提出的理论的新表述克服了这些困难。想象一下电介质中的每个材料粒子都附有一个重物和一个电池，并规定了一个虚拟位移场和一个虚拟电压场。与重量和惯性所做的虚拟功相关联，将标称应力定义为虚拟位移梯度的共轭。与电池所做的虚功相关，将标称电位移定义为虚电压梯度的共轭。该方法并不是从牛顿力学定律和麦克斯韦-法拉第静电学理论开始，而是将它们作为结果产生。这些定义导致了熟悉的解耦场方程。机电耦合通过材料定律进入理论。在流体电介质的极限情况下，该理论恢复了麦克斯韦应力。该方法是针对有限变形而开发的，并且适用于弹性和非弹性电介质。作为该理论的应用，我们讨论弹性电介质的材料定律，并研究叠加在给定场上的无穷小场，包括振动、波传播和分叉等现象。
Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell–Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.