This paper aims to build a constitutive model intended to describe the thermomechanical behavior
of shape memory alloys. This behavior presents many facets, among them we have considered the simple way of shape memory, which is one of most important
properties of shape memory alloys. Because of numerous stages of this effect, the
subject was divided into three independent parts. For each part, we
built the corresponding thermodynamic potential and we deduced the constitutive
equations. To make this model workable, we have developed an algorithm. The simulation
was performed using the NiTi as shape memory alloy.
Cite this paper
B. Meddour, H. Zedira and H. Djebaili, "One Dimensional Modeling of the Shape Memory Effect," Modeling and Numerical Simulation of Material Science
, Vol. 3 No. 4, 2013, pp. 124-128. doi: 10.4236/mnsms.2013.34017
 B. Halphen and Q. S. Nguyen, “Sur les Matériaux Standards Generalisés,” Journal de Mécanique, Vol. 14, 1975, pp. 39-63.
 C. Lexcellent and C. Licht, “Some Remarks on the Modelling of the Thermomechanical Behavior of Shape Memory Alloys,” Journal de Physique IV, Vol.1, No. C4, 1991, pp. C4-35-C4-39.
 D. C. Edelen, “On the Characterization of Fluxes in Nonlinear Irreversible Thermodynamics,” International Journal of Engineering Science, Vol. 12, No. 5, 1974, pp. 397-411. http://dx.doi.org/10.1016/0020-7225(74)90050-0
 K. Tanaka and S. Nagaki, “A Thermomechanical Description of Materials with Internal Variables in the Process of Phase Transformations,” Ingenieur-Archiv, Vol. 51, No. 5, 1982, pp. 287-299.
 C. Chu and R. D. James, “Analysis of Microstructures in Cu-14.0%Al-3.9%Ni by Energy Minimization,” Proceedings of the ICOMAT-95, Vol. 5, No. C8, 1995, pp. C8- 143-C8-149.
 R. D. James, R. V. Kohn and T. W. Shield, “Modeling of Branched Needle Microstructures at the Edge of a Martensite Laminate,” Proceedings of the ICOMAT-95, Vol. 5, No. C8, 1995, pp. C8-253-C8-259.
 C. Lexcellent, B. C. Goo, Q. P. Sun and J. Bernardint, “Characterization, Thermomechanical Behaviour and Micromechanical-Based Constitutive Model of Shape-Memory Cu-Zn-Al Single Crystals,” Acta Materialia, Vol. 44, No. 9, 1996, pp. 3773-3780.
 S. Govindjee and G. J. Hall, “A Computational Model for Shape Memory Alloys,” International Journal of Solids and Structures, Vol. 37, No. 5, 2000, pp. 735-760.
 M. Berveiller, E. Patoor and M. Buisson, “Thermomechanical Constitutive Equations for Shape Memory Alloys,” Journal de Physique IV, Vol. 1, No. C4, 1991, pp. C4-387-C4-396.
 E. Patoor, A. Eberhardt and M. Berveiller, “On Micromechanics of Thermoelastic Phase Transition,” Proceedings of Plasticity 93: The 4th International Symposium on Plasticity and Its Applications, Baltimore, 19-23 July 1993.
 K. L. Ng and Q. P. Sun, “Stress-Induced Phase Transformation and Detwinning in NiTi Polycrystalline Shape Memory Alloy Tubes,” Mechanics of Materials, Vol. 38, No. 1-2, 2006, pp. 41-56.