Shape-memory alloys and effects: Types, functions, modeling, and applications: Mathematical models for shape memory materials

Smart Materials

Volumn , Issue , 2008, Pages 20-17-20-28

  Bernardini, Davide ^a   Pence, Thomas J ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b Michigan State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85056958370     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (37)

1. Auricchio, F., Taylor, R.L., and Lubliner, J. 1997. Shape-memory alloys: Macromodelling and numerical simulations of the superelastic behavior, Comp. Meth. Appl. Mech. Eng., 146, 281-312.
2. Ball, J.G. and James, R.D. 1987. Fine phase mixtures as minimizers of energy, Arch. Rat. Mech. Anal., 100, 13-52.
3. Bernardini, D. and Pence, T.J. 2002. Shape memory alloys: modeling, In: Encyclopedia of Smart Materials, vol. 2, pp. 964-980, Wiley, New York.
4. Bernardini, D. and Pence, T.J. 2002. Models for one-variant shape memory materials based on dissipation functions, Int. J. Nonlinear Mech., 37, 1299-1317.
5. Bernardini, D. and Pence, T.J. 2003. A multifield theory for the modeling of the macroscopic behavior of shape memory materials, In: Advances in Multifield Theories of Continua with Substructure, Capriz G. and Mariano P.M. (Eds.), pp. 199-242, Birkhauser, Boston, MA.
6. Bernardini, D. and Pence, T.J. 2005. Uniaxial modeling of multivariant shape-memory materials with internal sublooping using dissipation functions, Meccanica, 40, 339-364.
7. Bhattacharya, K. and Kohn, R.V. 1997. Elastic energy minimization and the recoverable strains of polycrystalline shapememory materials, Arch. Rat. Mech. Anal., 139, 99-180.
8. Bondaryev, E.N. and Wayman, C.M. 1988. Some stress-strain-temperature relationships for shape memory alloys, Metallur. Trans. A, 19A, 2407-2413.
9. Boyd, J.G. and Lagoudas, D.C. 1996. A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy, Int. J. Plasticity, 12, 805-842.
10. Brinson, L.C. 1993. One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable, J. Intell. Mater. Syst. Struct., 4, 229-242.
11. Chang, B.C., Shaw, J.A., and Iadicola, M.A. 2006. Thermodynamics of shape memory alloy wire: Modeling, experiments and applications, Cont. Mech. Therm., 18, 83-118.
12. De La Flor, S., Urbina, C., and Ferrando, F. 2006. Constitutive model of shape memory alloys; theoretical formulation and experimental validation, Mat. Sci. Eng A., 427, 112-122.
13. Elahina, M.H. and Ahmadian, M. 2005. An enhanced SMA phenomenological model: I. The shortcomings of the existing models, Smart Mater. Struct., 14, 1297-1308.
14. Falk, F. 1980. Model, free energy, mechanics and thermo dynamics of shape memory alloys, Acta Metallur., 28, 1773-1780.
15. Gao, X., Huang, M., and Brinson, L.C. 2000. A multivariant micromechanical model for SMAs. Part 1. Crystallographic issues for single crystal model, Int. J. Plasticity, 16, 1345-1369.
16. Green, A.E. and Naghdi, P.M. 1977. On thermodynamics and the nature of the second law, Proc. Roy. Soc. Lond. A, 357, 253-270.
17. Ikeda, T., Nae, F.A., Naito, H., and Matsuzaki, Y. 2004. Constitutive model for of shape memory alloys for unidirectional loading considering inner hysteresis loops, Smart Mater. Struct., 13, 916-925.
18. Ivshin, Y. and Pence, T.J. 1994a. A constitutive model for hysteretic phase transitions, Int. J. Eng. Sci., 32, 681-704.
19. Ivshin, Y. and Pence, T.J. 1994b. A thermomechanical model for a one-variant shape memory material, J. Intell. Mat. Syst. Struct., 5, 455-473.
20. Lacarbonara, W., Bernardini, D., and Vestroni, F. 2004. Nonlinear thermomechanical oscillations of shape memory devices, Int. J. Solids Struct., 41, 1209-1234.
21. Lagoudas, D.C., Entchev, P.B., Popov, P., Patoor, E., Brinson, L.C., and Gao, X. 2006. Shape memory alloys, Part II: Modeling of polycrystals, Mech. Materials, 38, 430-462.
22. Liang, C. and Rogers, C.A. 1990. One-dimensional thermomechanical constitutive relations for shape memory materials, J. Intell. Mat. Syst. Struct., 1, 207-234.
23. Likhacev, A.A. and Koval, Y.N. 1992. On the differential equation describing the hysteretic behavior of shape memory alloys, Scrip. Metallur. Mater., 27, 223-227.
24. Matsuzaki, Y. and Kamita, T. 1998. One-dimensional pseudoelastic theory of shape memory alloys, Smart Mater. Struct., 489-495.
25. Muller, I. and Seelecke, S. 2001. Thermodynamic aspects of shape memory alloys, Math. Computer Modelling, 34, 1307-1355.
26. Ortin, J. 1991. Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal, J. Appl. Phys., 71, 1454-1461.
27. Otsuka, K. and Shimizu, K. 1986. Pseudoelasticity and shape memory effects in alloys, Int. Metal Rev., 31, 93-114.
28. Patoor, E., Eberhardt, A., and Berveiller, M. 1988. Thermomechanical behavior of shape memory alloys, Arch. Mech., 40, 755-794.
29. Puglisi, G. and Truskinovsky, L. 2005. Thermodynamics of rate-independent plasticity, J. Mech. Phys. Solids, 53, 655-679.
30. Rajagopal, K.R. and Srinivasa, A.R. 1999. On the thermom echanics of shape memory wires, Z. Angew. Math. Phys., 50, 459-496.
31. Raniecki, B., Lexcellent, C., and Tanaka, K. 1992. Thermodynamic models for pseudoelastic behavior of shape memory alloys, Arch. Mech., 44, 261-288.
32. Roubicek, T. 2004. Models of microstructure evolution in shape memory alloys, In: Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials, Ponte Casteneda P., Telega J.J., and Gamblin B. (Eds.), NATO Science Series, Math. Phys. Chem. 170, pp. 65-106, Kluwer.
33. Shaw, J.A. and Kyriakides, S. 1995. Thermomechanical Aspects of NiTi, J. Mech. Phys. Solids, 43, 1243-1281.
34. Shaw, J.A. 2002. A thermomechanical model for a 1-D shape memory alloy wire with propagating instabilities, Int. J. Solids Struct, 39, 1275-1305.
35. Siredey, N., Patoor, E., Berveiller, M., and Eberhardt, A. 1999. Constitutive equations for polycrystalline thermoelastic shape memory alloys. Part I. Intragranular interactions and behavior of the grain, Int. J. Solids Struct., 36, 4289-4315.
36. Tanaka, K., Kobayashi, S., and Sato, Y. 1986. Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys, Int. J. Plasticity, 2, 59-72.
37. Wu, X. and Pence, T.J. 1998. Two variant modeling of shape memory materials: Unfolding a phase diagram triple point, J. Intell. Mat. Syst. Struct., 9, 335-354.