By means of the Ginzburg–Landau theory of phase transitions, we study a nonisothermal model to characterize the austenite-martensite transition in shape memory alloys. In the first part of this paper, the one-dimensional model proposed by Berti et al. [“Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model,” Physica D 239, 95 (2010)] is modified by varying the expression of the free energy. In this way, the description of the phenomenon of hysteresis, typical of these materials, is improved and the related stress-strain curves are recovered. Then, a generalization of this model to the three-dimensional case is proposed and its consistency with the principles of thermodynamics is proven. Unlike other three-dimensional models, the transition is characterized by a scalar valued order parameter φ and the Ginzburg–Landau equation, ruling the evolution of φ, allows us to prove a maximum principle, ensuring the boundedness of φ itself.

Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys

GRANDI, Diego
2010

Abstract

By means of the Ginzburg–Landau theory of phase transitions, we study a nonisothermal model to characterize the austenite-martensite transition in shape memory alloys. In the first part of this paper, the one-dimensional model proposed by Berti et al. [“Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model,” Physica D 239, 95 (2010)] is modified by varying the expression of the free energy. In this way, the description of the phenomenon of hysteresis, typical of these materials, is improved and the related stress-strain curves are recovered. Then, a generalization of this model to the three-dimensional case is proposed and its consistency with the principles of thermodynamics is proven. Unlike other three-dimensional models, the transition is characterized by a scalar valued order parameter φ and the Ginzburg–Landau equation, ruling the evolution of φ, allows us to prove a maximum principle, ensuring the boundedness of φ itself.
Berti, V.; Fabrizio, M.; Grandi, Diego
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11392/2362481
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