一类铁电模型的参变量变分原理及其应用

Parametrical variational principle and its application to a class of ferro-electric models

将参变量变分原理引入铁电问题。对一类借用了经典弹塑性理论中的概念和方法的多轴铁电模型建立基于Helmholtz自由能的参变量变分原理,可以有效处理传统变分原理中由非关联流动法则或屈服面不考虑材料系数变化所引起的切线模量非对称困难。相应于参变量变分原理,引入参数二次规划算法,可获得具有可靠数值稳定性的一套铁电算法。将该算法应用于一个具体的铁电模型,数值计算结果表明本文方法的有效性。

For the high complexity of the constitutive models of ferro-electrics, the efficiency and stability of the numerical methods must be paid full attention to when simulating the electro-mechanical behavior of ferro-electrics. The present work introduces the parametrical variational principle into the computation of ferroelectrics. A parametrical variational principle based on the Helmholtz free energy is established for a class of multi-axial phenomeno-logical ferro-electric constitutive models which adopts the basic concepts and theoretical framework of the traditional elasto-plasticity. The variational principle can effectively deal with the difficulty of non-symmetric tangent moduli which appears when the non-associated flow law or the yield-liked switching surface without considering the change of material moduli with domain switching is used. Corresponding parametric quadratic programming algorithm is introduced to present a new numerical scheme with reliable numerical stability. Applying the present numerical scheme on a typical ferro-electric constitutive model, the numerical results of the simulation of the hysteresis loop and the butterfly-shaped loop show the good performance of the present method.