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A new "flexible" 3D macroscopic model for shape memory alloys
Free energies and pseudo-elastic transitions for shape memory alloys
1. | Facoltà di Ingegneria, Università e-Campus, 22060 Novedrate (CO) |
2. | Dipartimento di Matematica, Università di Brescia, 25133 Brescia, Italy, Italy |
References:
[1] |
F. Auricchio, Considerations on the constitutive modeling of shape-memory alloys, in "Shape Memory Alloys: Advances in Modelling and Applications" (eds. F. Auricchio, L. Faravelli, G. Magonette and V. Torra), CMINE: Barcelona, (2002), 125-187. |
[2] |
A. Berti, C. Giorgi and E. Vuk, Free energies in one-dimensional models of magnetic transitions with hysteresis, Il Nuovo Cimento, B, 125 (2010), 371-394. |
[3] |
V. Berti, M. Fabrizio and D. Grandi, Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model, Physica D, 239 (2010), 95-102.
doi: 10.1016/j.physd.2009.10.005. |
[4] |
V. Berti, M. Fabrizio and D. Grandi, Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys, J. Math. Phys., 51 (2010), 062901.
doi: 10.1063/1.3430573. |
[5] |
L. C. Brinson, One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variables, Journal of Intelligent Material Systems and Structures, 4 (1993), 229-242.
doi: 10.1177/1045389X9300400213. |
[6] |
M. Fabrizio and A. Morro, "Electromagnetism of Continuous Media," Oxford University Press, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198527008.003.0010. |
[7] |
M. Fremond, Materiaux a memoire de forme, C. R. Acad. Sci. Paris Ser. II, 304 (1987), 239-244. |
[8] |
M. Fremond, "Non-smooth Thermomechanics," Springer-Verlag, Berlin, 2002.
doi: 10.1115/1.1497489. |
[9] |
V. I. Levitas and D. L. Preston, Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite$\leftrightarrow$martensite, Physical Review B, 66 (2002), 134-206. |
[10] |
S. Miyazaki, Development and characterization of shape memory alloys, in "CISM Courses and Lectures: Shape Memory Alloys," 351. Springer: Wien, NewYork, (1996), 69-143. |
[11] |
I. Müller, Thermodynamics of ideal pseudoelasticity, Journal de Physique IV, C2-5 (1995), 423-431. |
[12] |
I. Müller and S. Seelecke, Thermodynamic aspects of shape memory alloys, Math. Comp. Modelling, 34 (2001), 1307-1355.
doi: 10.1016/S0895-7177(01)00134-0. |
[13] |
F. Nishimura, N. Watanabe, T. Watanabe and K. Tanaka, Transformation conditions in an Fe-based shape memory alloy under tensile-torsional loads: Martensite start surface and austenite start/finish planes, Material Science and Engineering, A264 (1999), 232-244.
doi: 10.1016/S0921-5093(98)01093-4. |
[14] |
C. M. Wayman, Shape memory and related phenomena, Progress in Materials Science, 36 (1992), 203-224.
doi: 10.1016/0079-6425(92)90009-V. |
[15] |
J. C. Willems, Dissipative dynamical systems - Part I: General theory, Arch. Rational Mech. Anal., 45 (1972), 321-351.
doi: 10.1007/BF00276493. |
show all references
References:
[1] |
F. Auricchio, Considerations on the constitutive modeling of shape-memory alloys, in "Shape Memory Alloys: Advances in Modelling and Applications" (eds. F. Auricchio, L. Faravelli, G. Magonette and V. Torra), CMINE: Barcelona, (2002), 125-187. |
[2] |
A. Berti, C. Giorgi and E. Vuk, Free energies in one-dimensional models of magnetic transitions with hysteresis, Il Nuovo Cimento, B, 125 (2010), 371-394. |
[3] |
V. Berti, M. Fabrizio and D. Grandi, Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model, Physica D, 239 (2010), 95-102.
doi: 10.1016/j.physd.2009.10.005. |
[4] |
V. Berti, M. Fabrizio and D. Grandi, Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys, J. Math. Phys., 51 (2010), 062901.
doi: 10.1063/1.3430573. |
[5] |
L. C. Brinson, One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variables, Journal of Intelligent Material Systems and Structures, 4 (1993), 229-242.
doi: 10.1177/1045389X9300400213. |
[6] |
M. Fabrizio and A. Morro, "Electromagnetism of Continuous Media," Oxford University Press, Oxford, 2003.
doi: 10.1093/acprof:oso/9780198527008.003.0010. |
[7] |
M. Fremond, Materiaux a memoire de forme, C. R. Acad. Sci. Paris Ser. II, 304 (1987), 239-244. |
[8] |
M. Fremond, "Non-smooth Thermomechanics," Springer-Verlag, Berlin, 2002.
doi: 10.1115/1.1497489. |
[9] |
V. I. Levitas and D. L. Preston, Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite$\leftrightarrow$martensite, Physical Review B, 66 (2002), 134-206. |
[10] |
S. Miyazaki, Development and characterization of shape memory alloys, in "CISM Courses and Lectures: Shape Memory Alloys," 351. Springer: Wien, NewYork, (1996), 69-143. |
[11] |
I. Müller, Thermodynamics of ideal pseudoelasticity, Journal de Physique IV, C2-5 (1995), 423-431. |
[12] |
I. Müller and S. Seelecke, Thermodynamic aspects of shape memory alloys, Math. Comp. Modelling, 34 (2001), 1307-1355.
doi: 10.1016/S0895-7177(01)00134-0. |
[13] |
F. Nishimura, N. Watanabe, T. Watanabe and K. Tanaka, Transformation conditions in an Fe-based shape memory alloy under tensile-torsional loads: Martensite start surface and austenite start/finish planes, Material Science and Engineering, A264 (1999), 232-244.
doi: 10.1016/S0921-5093(98)01093-4. |
[14] |
C. M. Wayman, Shape memory and related phenomena, Progress in Materials Science, 36 (1992), 203-224.
doi: 10.1016/0079-6425(92)90009-V. |
[15] |
J. C. Willems, Dissipative dynamical systems - Part I: General theory, Arch. Rational Mech. Anal., 45 (1972), 321-351.
doi: 10.1007/BF00276493. |
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