The present work proposes a phenomenological level-set model for shape memory alloys within the framework of internal variable theory and continuum thermomechanics. While the majority of constitutive models for shape memory alloys assume the martensitic volume fraction as an internal variable, in this study a level-set function is chosen to be the internal variable. Such a choice allows to account, on average, for the microstructural changes within the material by representing in an implicit manner the interfaces between different phases. Utilizing consistent thermodynamical arguments within the framework of canonical thermomechanics, the evolution equation for the level-set function is derived. Then, the model is implemented in a one dimensional case, where simple evolution equations are proposed reproducing certain characteristics of shape memory alloys, such as the pseudoelastic effect, the strain-temperature hysteresis, the one-way shape memory effect and hardening effects. Also, application of the model on functional fatigue phenomenon is thoroughly inspected. This new constitutive level-set model provides extreme flexibility and seems to be very promising for future research.

中文翻译：

---

形状记忆合金的本构水平集模型

目前的工作在内变量理论和连续热力学的框架内提出了形状记忆合金的现象学水平集模型。虽然大多数形状记忆合金的本构模型将马氏体体积分数假定为内部变量，但在本研究中，选择水平集函数作为内部变量。通过以隐式方式表示不同相之间的界面，这种选择允许平均考虑材料内的微观结构变化。利用规范热力学框架内的一致热力学参数，导出了水平集函数的演化方程。然后，模型在一维情况下实现，其中提出了简单的演化方程来再现形状记忆合金的某些特性，例如伪弹性效应、应变-温度滞后、单向形状记忆效应和硬化效应。此外，彻底检查了模型在功能性疲劳现象上的应用。这种新的本构水平集模型提供了极大的灵活性，似乎对未来的研究非常有希望。