Abstract

This work proposes a phenomenological level-set model for ferromagnetic shape-memory alloys (FSMAs), developed under consistent thermodynamic analysis. A set of adequate internal and external variables is chosen so as to describe the rate-independent magneto-mechanical response of a FSMA single crystal. Almost every phenomenological model in bibliography adopts martensitic volume fractions as internal variables. The novelty of this work is the introduction of a continuous level-set function as an internal variable of state, which accounts implicitly for the dissipative twin boundary motion in the evolution of inelastic reorientation of martensitic variants. Following the usual internal variable formalism within the framework of standard magnetomechanics, the evolution equations for the level-set function are derived for the forward and reverse variant reorientation processes. The model is implemented in a two-dimensional special case, where the reduced equations are numerically solved capturing the important effects of stress-induced and magnetic field-induced martensitic variant reorientation, such as magnetization hysteresis, pseudoelastic/partial pseudoelastic behavior and magnetic shape-memory effect. The proposed constitutive model is capable of explaining the constitutive response caused by the reorientation of martensitic variants in FSMAs and may be further improved so as to be implemented in even more complicated situations, such as dynamic and rate-dependent analysis.

中文翻译：

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铁磁形状记忆合金的本构能级模型

摘要

这项工作提出了铁磁形状记忆合金（FSMA）的现象学水平集模型，该模型是在一致的热力学分析下开发的。选择一组适当的内部和外部变量，以描述FSMA单晶的与速率无关的磁机械响应。在参考书目中，几乎所有的现象学模型都采用马氏体体积分数作为内部变量。这项工作的新颖之处在于引入了一个连续的水平集函数作为状态的内部变量，它隐含地解释了马氏体变体的非弹性重取向演变过程中的耗散孪晶边界运动。遵循标准磁力学框架内通常的内部变量形式主义，推导了水平集函数的演化方程，用于正向和反向变体重新定向过程。该模型是在二维特殊情况下实施的，其中对简化的方程进行了数值求解，从而捕获了应力诱发和磁场诱发的马氏体变体重新定向的重要影响，例如磁化磁滞，伪弹性/部分伪弹性行为以及磁性形状。记忆效应。所提出的本构模型能够解释由FSMA中马氏体变体的重新定向所引起的本构响应，并且可以进一步加以改进，以便在甚至更复杂的情况下实施，例如动态和速率依赖分析。其中简化的方程式通过数值求解得到了应力诱导和磁场诱导的马氏体变体重新定向的重要效果，例如磁化磁滞，伪弹性/部分伪弹性行为和磁形状记忆效应。所提出的本构模型能够解释由FSMA中马氏体变体的重新定向所引起的本构响应，并且可以进一步加以改进，以便在甚至更复杂的情况下实施，例如动态和速率依赖分析。其中简化的方程式通过数值求解得到了应力诱导和磁场诱导的马氏体变体重新定向的重要效果，例如磁化磁滞，伪弹性/部分伪弹性行为和磁形状记忆效应。所提出的本构模型能够解释由FSMA中马氏体变体的重新定向所引起的本构响应，并且可以进一步加以改进，以便在甚至更复杂的情况下实施，例如动态和速率依赖分析。