Meccanica (2010) 45: 797–807 DOI 10.1007/s11012-010-9286-z A non isothermal Ginzburg-Landau model for phase transitions in shape memory alloys F. Daghia · M. Fabrizio · D. Grandi Received: 13 January 2009 / Accepted: 11 February 2010 / Published online: 9 June 2010 © Springer Science+Business Media B.V. 2010 Abstract A thermodynamical model for martensitic phase transitions in shape memory alloys is formulated in this paper in the framework of the Ginzburg-Landau approach to phase transitions. A single order parame- ter is chosen to represent the austenite parent phase and two mirror related martensite variants. A free energy previously proposed in the literature (Levitas et al. in Phys. Rev. B 66:134206, 2002; Phys. Rev. B 66:134207, 2002; Phys. Rev. B 68:134201, 2003) is employed, in its simplest form, as the main constitu- tive content of the model. In this paper we treat time- dependent Ginzburg-Landau equation as a balance law on the structure order and we couple it to a energy bal- ance equation, thus allowing to account of heat trans- fer processes. We obtain a coupled thermo-mechanical problem whose consistency with the Second Law is verified. Finally, a suggestion to expand the proposed model to a full three-dimensional description which accounts for the formation of different martensite variants is proposed. F. Daghia DISTART Department, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy M. Fabrizio ( ) · D. Grandi Mathematics Department, University of Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy e-mail: fabrizio@dm.unibo.it Keywords Shape memory alloys · Phase transitions · Thermodynamics 1 Introduction Shape memory alloys (SMA) are metal alloys which exhibit peculiar material properties, known as shape memory effect (SME) and superelasticity (SE) [1]. The shape memory effect occurs at low temperatures and consists in the ability to recover large residual de- formations after the material is heated above a charac- teristic temperature. Superelasticity, on the other hand, takes place at high temperatures; it is the ability to re- cover large deformations by simply removing the ap- plied load. These two properties are summarized in the graph in Fig. 1. Shape memory properties were first observed in gold-cadmium alloys in the 1930s [2, 3], however a widespread interest in these materials had to wait until the discovery of the shape memory effect in a nickelti- tanium alloy [4]. The shape memory alloys properties Fig. 1 Shape memory effect (SME) and superelasticity (SE)