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针对铁电试样电畴随机分布的情况,提出了多电畴力学模型.模型中极化后的铁电试样由许多靠近极化电场方向的随机分布的电畴所组成.每个电畴看作是一个单元,每个单元的翻转驱动力计算公式中的应力和电场强度采用宏观应力和电场强度,利用标定的电畴翻转驱动力与电畴翻转体积分数之间的强化关系,计算出每个单元的电畴翻转体积分数,将外加应力和电场强度和求得的电畴翻转体积分数代入本构方程就可以求得各个单元的应变和电位移,对所有单元进行体积平均得到铁电试样的宏观本构响应.同时也对铁电试样的非线性本构行为进行了有限元模拟.在有限元计算中,首先由宏观应力和电场强度计算出每个单元电畴翻转驱动力,进而得到各单元电畴翻转体积分数,就可以针对本次加载进行有限元计算,计算中考虑到各单元自发极化方向不同而引起的交互作用得到各单元的应力、应变和电位移,体积平均求得试样的宏观本构行为.根据以上两种方法进行了计算,计算结果包括单轴力加载和单轴电加载下的应力应变曲线、应力电位移曲线以及力电耦合加载下铁电试样的电滞回线、蝶形曲线,理论预测与实验结果符合良好.
Aiming at the random distribution of the ferroelectric domains, a multi-domain mechanical model is proposed, in which the polarized ferroelectric samples consist of a number of randomly distributed domains close to the direction of the polarized electric field. Each domain As a unit, the stress and electric field strength in the calculation formula of the turnover driving force of each unit adopts the macroscopic stress and the electric field strength, and by using the intensified relationship between the driving force of the electric field reversal and the turnover volume fraction of the domain, Each unit of the domain inversion volume fraction, the applied stress and electric field strength and domain inversion volume fraction obtained into the constitutive equation can be obtained for each unit of the strain and electric displacement, the volume of all units were averaged to obtain ferroelectric In addition, the nonlinear constitutive behavior of ferroelectric samples was also simulated by finite element method. In the finite element calculation, the driving force of domain inversion per unit was first calculated from the macroscopic stress and electric field intensity , And then get each unit domain inversion volume fraction, you can for this load finite element calculation, taking into account the unit of the spontaneous polarization direction of the interaction caused by different To each unit of stress, strain and displacement, the volume average obtained macroscopic constitutive behavior of the sample.According to the above two methods were calculated, the calculation results include the uniaxial force and uniaxial load stress-strain curve, The stress-displacement curve and the hysteresis curve and the butterfly curve of the ferroelectric material under the electromechanical coupling load are in good agreement with the experimental results.