This work proposes a thermodynamic-based constitutive model for shape memory alloy, which captures the gradual variation in stress–strain response from the shape memory effect to the pseudoelastic effect. The present model also provides a framework for modeling various other responses, such as strain temperature hysteresis and thermally induced strain recovery effect. The model classifies the different phases of the material, such as twinned martensite, detwinned martensite, and austenite, and the mix of these phases using only two internal variables, namely austenite volume fraction and inelastic martensite strain. The proposed model shows that introducing two independent yield conditions corresponding to each internal variable is sufficient to describe all the phase transformations. After presenting the theoretical framework of the model, the procedure for numerical implementation has been discussed. The simulation shows the gradual variation in the stress–strain curve at different temperatures in the phase transformation range and is observed to have an adequate quantitative agreement with the experimental data The model is further implemented for different shape memory alloys to show the possibility of the generalized framework for this class of materials. In addition, the capability of simulating other phenomena of SMA, such as strain response for thermal loading at constant stress and the complete response of strain recovery in shape memory behavior, is also presented.

这项工作提出了一种基于热力学的形状记忆合金本构模型，该模型捕获了从形状记忆效应到伪弹性效应的应力应变响应的逐渐变化。本模型还提供了用于模拟各种其他响应的框架，例如应变温度滞后和热致应变恢复效应。该模型对材料的不同相进行分类，例如孪生马氏体、解孪生马氏体和奥氏体，并且仅使用两个内部变量（即奥氏体体积分数和非弹性马氏体应变）对这些相进行混合。所提出的模型表明，引入与每个内部变量相对应的两个独立的屈服条件足以描述所有相变。在提出模型的理论框架之后，讨论了数值实现的过程。模拟显示了相变范围内不同温度下应力-应变曲线的逐渐变化，并观察到与实验数据有足够的定量一致性。该模型进一步应用于不同的形状记忆合金，以显示广义化的可能性此类材料的框架。此外，还介绍了模拟 SMA 其他现象的能力，例如恒定应力下热载荷的应变响应以及形状记忆行为中应变恢复的完整响应。