The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

本文的目的是建立在连续热力学框架内可变形铁电体的磁滞特性的矢量值速率型模型。与电弹性和压电不同，在铁电中，极化和电场同时是独立变量，因此本构函数依赖于两者。这种观点自然与以下事实有关：磁滞回线是极化电场平面中的闭合曲线。为了通用，允许发生材料的变形和对温度的依赖性。要求本构函数与客观性原理和热力学第二定律一致。客观性意味着，本构方程在欧几里得框架集内是不变的。除其他结果外，第二定律要求通过微分方程具有关于极化和电场之间关系的一般性质。该方程式显示出一个完全由两个量表征的相关性：自由能和与磁滞的耗散特性有关的函数。结果，不同的磁滞模型可能具有相同的自由能。热力学兼容的型号，然后通过和耗散部分的自由能量的适当的选择来决定。相应地，绘制了主要和次要磁滞回线。第二定律要求通过微分方程具有关于极化和电场之间关系的一般性质。该方程式显示出一个完全由两个量表征的相关性：自由能和与磁滞的耗散特性有关的函数。结果，不同的磁滞模型可能具有相同的自由能。热力学兼容的型号，然后通过和耗散部分的自由能量的适当的选择来决定。相应地，绘制了主要和次要磁滞回线。第二定律要求通过微分方程具有关于极化和电场之间关系的一般性质。该方程式显示出一个完全由两个量表征的相关性：自由能和与磁滞的耗散特性有关的函数。结果，不同的磁滞模型可能具有相同的自由能。热力学兼容的型号，然后通过和耗散部分的自由能量的适当的选择来决定。相应地，绘制了主要和次要磁滞回线。热力学兼容的型号，然后通过和耗散部分的自由能量的适当的选择来决定。相应地，绘制了主要和次要磁滞回线。热力学兼容的型号，然后通过和耗散部分的自由能量的适当的选择来决定。相应地，绘制了主要和次要磁滞回线。