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; 55:12551264), 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.