A three-dimensional model of the thermomechanical behavior of shape memory alloys

• Published in: Journal of the mechanics and physics of solids Vol. 55; no. 11; pp. 2455 - 2490
• Main Authors: Zaki, Wael, Moumni, Ziad
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2007; Elsevier
• Subjects: Engineering Sciences; Finite elements; Generalized standard materials; Macro-scale modeling; Thermomechanical SMA behavior; Three-dimensional structure analysis; Three-dimensional structure analysis; Generalized standard materials; Finite elements; Macro-scale modeling; Thermomechanical SMA behavior
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2007.03.012

A new macro-scale model of shape memory alloys is developed within the framework of generalized standard materials with internal constraints [Moumni, Z., 1995. Sur la modélisation du changement de phase à l’état solide. Ph.D. Thesis, École Nationale Supérieure des Ponts et Chaussées]. It is shown that the introduction of two state variables: the martensite volume fraction and the martensite orientation strain tensor, is sufficient to account for several effects exhibited by SMAs subject to thermomechanical loading, namely: self-accommodation, orientation and reorientation or martensite, as well as superelasticity and one-way shape memory. These phenomena are simulated using the same set of constitutive equations and evolution laws. A simple procedure for identifying the parameters of the model is described in detail and a validation against experimental data is conducted. The model is then used to analyze a 3D SMA structure representing a superelastic stent. Cyclic loading and other pertaining phenomena like training and two-way shape memory are considered in the second part of this paper.