A robust integration-algorithm for a finite-strain shape-memory-alloy superelastic model

An interesting feature of shape-memory alloys (SMA) is the superelastic effect, that is, the ability to undergo large deformations in loading–unloading cycles without showing permanent deformations. Due to this macroscopic behavior, not present in traditional materials, shape-memory alloys are exploited in innovative applications, often requiring the use of design tools. The present work proposes an efficient and robust solution algorithm to be used during the design of SMA-based devices through the use of classical computational tools such as the finite element method. To reach this goal, we review a constitutive model able to reproduce the superelastic behavior at finite strains. We then discuss a solution algorithm for the corresponding time-discrete model. Cast within the return-map family, the adopted approach pays particular attention to the overall algorithmic robustness and to the possibility of an efficient implementation. To properly test the proposed approach, we start solving a series of severe one-dimensional tests. We then also simulate a complex three-dimensional problem, relative to an orthodontic archwire.