In this study, a constitutive model based on Liang-Rogers’s relations is developed to characterize the effect of the excitation frequency in the hysteresis of shape memory alloys. Shape memory alloys are good candidates as smart actuators because of their high strain and power density, although the complex hysteresis behavior barricades their usage. Although constitutive models are one of the most potent methods to predict the shape memory alloys behavior, they cannot consider the effect of excitation frequency in active applications. In this paper, the Liang-Rogers model is modified to consider this effect using a linear relation between the excitation frequency and martensite transformation temperatures. A shape memory alloy-driven actuator as a morphing wing is employed to characterize the frequency effect on shape memory alloy hysteresis. Experimental results show that the hysteresis is widened when the excitation frequency increases. The modeling results show that the original model significantly fails to predict the correct behavior when the frequency increases, whereas the proposed model can adequately handle the frequency effect on the behavior of the shape memory alloy-driven actuator.

中文翻译：

---

形状记忆合金滞后的频率相关本构模型的开发

在这项研究中，开发了基于 Liang-Rogers 关系的本构模型来表征激发频率对形状记忆合金滞后的影响。形状记忆合金因其高应变和功率密度而成为智能执行器的良好候选者，尽管复杂的滞后行为阻碍了它们的使用。尽管本构模型是预测形状记忆合金行为的最有效方法之一，但它们无法考虑激励频率在主动应用中的影响。在本文中，使用激发频率和马氏体转变温度之间的线性关系修改了 Liang-Rogers 模型以考虑这种影响。采用形状记忆合金驱动的致动器作为变形翼来表征频率对形状记忆合金滞后的影响。实验结果表明，当激励频率增加时滞后变宽。建模结果表明，当频率增加时，原始模型明显无法预测正确的行为，而所提出的模型可以充分处理频率对形状记忆合金驱动的致动器行为的影响。