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

An interesting feature of shape-memory alloys (SMA) is the superelastic eff ect, that is, the ability to undergo large deformations in loading-unloadin g cycles without showing permanent deformations. Due to this macroscopic be havior, not present in traditional materials, shape-memory alloys are explo ited in innovative applications, often requiring the use of design tools. T he present work proposes an efficient and robust solution algorithm to be u sed during the design of SMA-based devices through the use of classical com putational 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 approac h pays particular attention to the overall algorithmic robustness and to th e possibility of an efficient implementation. To properly test the proposed approach, we start solving a series of severe one-dimensional tests. We th en also simulate a complex three-dimensional problem, relative to an orthod ontic archwire. (C) 2001 Elsevier Science Ltd. All rights reserved.