Thermo-mechanical evolution of shape memory alloys
Authors:
Pierluigi Colli, Michel Frémond and Augusto Visintin
Journal:
Quart. Appl. Math. 48 (1990), 31-47
MSC:
Primary 73B30; Secondary 35R35, 80A20
DOI:
https://doi.org/10.1090/qam/1040232
MathSciNet review:
MR1040232
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Abstract: In certain alloys, after deformation the original shape can be recovered just by thermal means. This shape memory behaviour can be interpreted as the effect of an austenite-martensite phase transition. We model this phenomenon by assuming the free energy to depend on the volumetric proportions of the different phases.
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H. Brézis, Operatéurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies 5, North-Holland, Amsterdam-London, 1973
H. Brézis, Problèmes unilatéraux, J. Math. Pures Appl. 51, 1–168 (1972)
F. Falk, Martensitic domain boundaries in shape-memory alloys as solitary waves, J. Physique, C4 Suppl. 12, 43, 3–15 (1982)
M. Frémond, Matériaux à mémoire de forme, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 304, 239–244 (1987)
M. Frémond and P. Nicolas, Hystérésis dans les milieux poreux humides non saturés, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 305, 741–746 (1987)
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MSI Workshop: The mathematical analysis of material microstructure, Cornell University, June 15–18, 1988
J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967
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M. Achenbach and I. Müller, Model for shape memory, J. Physique, C4 Suppl. 12, 43, 163–167 (1982)
H. W. Alt, K. H. Hoffmann, M. Niezgodka, and J. Sprekels, A numerical study of structural phase transitions in shape memory alloys, Preprint No 90, Institut für Mathematik, Augsburg University, 1985
S. Antman, J. L. Ericksen, D. Kinderlehrer, and I. Müller, eds., Metastability and Incompletely Posed Problems, Springer-Verlag, Berlin, 1987
D. Blanchard, M. Frémond, and A. Visintin, Phase change with dissipation, Thermomechanical Coupling in Solids, H. D. Bui and Q. S. Nguyen eds., North Holland, 1987, pp. 411–418
H. Brézis, Operatéurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies 5, North-Holland, Amsterdam-London, 1973
H. Brézis, Problèmes unilatéraux, J. Math. Pures Appl. 51, 1–168 (1972)
F. Falk, Martensitic domain boundaries in shape-memory alloys as solitary waves, J. Physique, C4 Suppl. 12, 43, 3–15 (1982)
M. Frémond, Matériaux à mémoire de forme, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 304, 239–244 (1987)
M. Frémond and P. Nicolas, Hystérésis dans les milieux poreux humides non saturés, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 305, 741–746 (1987)
M. Frémond and A. Visintin, Dissipation dans le changement de phase. Surfusion. Changement de phase irréversible, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 301, 1265–1268 (1985)
P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus—$^{0}$ partie, Théorie du second gradient, J. Mécanique 12, 235–274 (1973)
G. Guénin, Alliages à mémoire de forme, Technique de l’ingenieur, M 530, Paris, 1986
G. Herget, M. Müllner, G. Eckold, H. Tietze, and W. Assmus, Strukturelle Phasenübergäange der Formgedächtnislegierung NiTi, Jahresbericht 1987 des Inst, für Kernphysik, p. 77, Johann Wolfgang Göthe Universität, Frankfurt/Main, 1987
MSI Workshop: The mathematical analysis of material microstructure, Cornell University, June 15–18, 1988
J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967
M. Niezgodka and J. Sprekels, Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys, Math. Methods Appl. Sci. 10, 197–223 (1988)
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Article copyright:
© Copyright 1990
American Mathematical Society
