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EnglishBy 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.
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| Data di pubblicazione: | 2010 | |
| Titolo: | Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys | |
| Autori: | Berti, V.; Fabrizio, M.; Grandi, D. | |
| Rivista: | JOURNAL OF MATHEMATICAL PHYSICS | |
| Parole Chiave: | Martensitic phase transitions; Stress-strain relations; Free energy; Shape-memory effect; Phase transitions | |
| Abstract in inglese: | 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. | |
| Digital Object Identifier (DOI): | 10.1063/1.3430573 | |
| Handle: | http://hdl.handle.net/11392/2362481 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
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