A three‐dimensional model describing stress‐temperature induced solid phase transformations: solution algorithm and boundary value problems

An always increasing knowledge on material properties as well as a progressively more sophisticated production technology make shape memory alloys (SMA) extremely interesting for the industrial world. At the same time, SMA devices are typically characterized by complex multi‐axial stress states as well as non‐homogeneous and non‐isothermal conditions both in space and time. This aspect suggests the finite element method as a useful tool to help and improve application design and realization. With this aim, we focus on a three‐dimensional macroscopic thermo‐mechanical model able to reproduce the most significant SMA features (Int. J. Numer. Methods Eng. 2002; 55 : 1255–1264), proposing a simple modification of such a model. However, the suggested modification allows the development of a time‐discrete solution algorithm, which is more effective and robust than the one previously discussed in the literature. We verify the computational tool ability to simulate realistic mechanical boundary value problems with prescribed temperature dependence, studying three SMA applications: a spring actuator, a self‐expanding stent, a coupling device for vacuum tightness. The effectiveness of the model to solve thermo‐mechanical coupled problems will be discussed in a forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd.     

基于塑性理论的形状记忆合金本构模型、试验和数值模拟

通过拉伸试验,研究了超弹性形状记忆合金（SMA）丝在不同应变幅值反复加卸载条件下的滞回变形行为。在测得试验数据的基础上,针对目前广泛使用的SMA Graesser＆Cozzarelli模型仅描述了小应变情况下SMA特性,而在大应变下SMA马氏体的硬化特性不能得到描述的问题,提出了修正的SMA本构模型,并把模型拟合结果和实验数据进行了比较分析。结果表明,模型数值拟合结果和试验数据吻合很好,可以很好地描述SMA在不同应变幅值下的应力-应变关系;且模型形式简单,概念明确,参数容易得到,具有一定的工程应用价值。