Journal of the Mechanics and Physics of Solids 55 (2007) 2427–2454 A 3D model of the cyclic thermomechanical behavior of shape memory alloys Wael Zaki, Ziad Moumni à Unite´de Me´canique, E ´ cole Nationale Supe´rieure de Techniques Avance´es, 91761 Palaiseau, France Received 16 November 2006; received in revised form 21 March 2007; accepted 25 March 2007 Abstract The model in the first part of this paper is extended to account for SMA behavior under cyclic loading. To this end, three new state variables are introduced: internal stress B, residual strain e r and cumulated martensite volume fraction z e . Several parameters of the extended model depend on z e , making them evolve with cyclic phase change. Cyclic SMA effects including training and two-way shape memory are accounted for and several numerical simulations are provided and validated in the case of cyclic superelasticity. r 2007 Elsevier Ltd. All rights reserved. Keywords: Cyclic loading; Training; Two-way shape memory; Residual strain; Internal stress 1. Introduction Shape memory alloys (or SMAs) are used in a wide range of applications as actuators, biomedical stents, artificial muscles for microrobots, etc. These components usually operate under cyclic thermomechanical loading, hence the importance of a reliable prediction of the 3D cyclic material response and the considerable number of related works. In this regard, Abeyaratne and Kim (1997) accounted for the effect of training on martensite formation by modifying the thermodynamic driving force associated with phase change. This was done by altering the energy barriers between austenite and two ARTICLE IN PRESS www.elsevier.com/locate/jmps 0022-5096/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2007.03.011 à Corresponding author. Tel.: +33 169319724; fax: +33 169319906. E-mail address: ziad.moumni@ensta.fr (Z. Moumni).