On the correspondence between micromechanical models for isothermal pseudoelastic response of shape memory alloys and the Preisach model for hysteresis

Mathematics and Mechanics of Solids

Volumn 2, Issue 4, 1997, Pages 405-440

  Lagoudas, D C ^a   Bhattacharyya, A ^a  

^a Texas AandM University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTUATORS; ELASTICITY; HYSTERESIS; MATHEMATICAL MODELS; PHASE TRANSITIONS; POLYCRYSTALLINE MATERIALS; POLYCRYSTALS; SHAPE MEMORY EFFECT; SINGLE CRYSTALS;

PREISACH MODEL; SHAPE MEMORY ALLOYS;

COMPOSITE MICROMECHANICS;

EID: 0031334629     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128659700200403     Document Type: Article

References (53)

1. Preisach, F.: Uber die Magnetische Nachwirkung. Zietschrift fur Physik, 94, 277 (1935).
2. Batdorf, S. B. and Budiansky, B.: A mathematical theory of plasticity based on the concept of slip. NACA TN-1871 (1949).
3. Hill, R.: The Mathematical Theory of Plasticity, Clarendon, Oxford, 1950.
4. Weschler, M. S., Lieberman, D. S., and Read, T. A.: On the theory of formation of martensite. Trans. TMS-AIME, 197, 1503 (1953).
5. Bowles, J. S. and Mackenzie, J. K.: The crystallography of martensitic transformtions. Acta Metall., 2, 129 (1954).
6. Roscoe, R.: The viscosity of suspensions of rigid spheres. Br. J. Appl. Phys., 3, 567 (1954).
7. Lin, T. H.: Analysis of elastic and plastic strains of a face-centered cubic crystal. J. Mech. Phys. Solids, 5, 143 (1957).
8. Buehler, W. J. and Wiley, R. C.: Nickel-base alloys. U.S. patent 3,174,851 (1965).
9. Hill, R.: Continuum micromechanics of elastoplastic polycrystals. J. Mech. Phys. Solids, 13, 89 (1965).
10. Jackson, C. M., Wagner, H. J., and Wasilewski, R. J.: 55-nitinol - The alloy with a memory: Its physical metallurgy, properties and applications. NASA-SP 5110 (1972).
11. Mori, T. and Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall., 231, 571 (1973).
12. Perkins, J.: Shape Memory Effects in Alloys, Plenum, New York, 1975.
13. Christensen, R. M.: Mechanics of Composite Materials, John Wiley, New York, 1979.
14. Mura, T.: Micromechanics of Defects in Solids, Martinus Nijhoff, Amsterdam, 1980.
15. Kane, T. R., Likins, P. W., and Levinson, D. A.: Spacecraft Dynamics, McGraw-Hill, New York, 1983.
16. Wayman, C. M.: Phase transformations, nondiffusive, in Physical Metallurgy, p. 1031, eds., R. W. Cahn & P. Haasen, North-Holland Physics, New York, 1983.
17. Coleman, B. D. and Hodgdon, M. L.: On a class of constitutive relations for ferromagnetic hysteresis. Arch. Rational Mech. Anal., 99, 375 (1987).
18. Tanaka, K.: A thermomechanical sketch of shape memory effect: One-dimensional tensile behavior. Res Mechanica, 18, 251 (1986).
19. Patoor, E., Eberhardt, A., and Berveiller, M.: Potentiel pseudoelastique et plasticite de transformation martenistique dans les mono-et polycristaux metalliques. Acta Metall., 35(11), 2779 (1987).
20. Jaeger, C. A. and Rogers, C. A.: An overview of smart materials, structures and mathematical issues, in Proc. U.S. Army Research Office Workshop on Smart Materials, Structures and Mathematical Issues, Virginia Polytechnic Institute and State University, Blacksburg, 1987.
21. Sato, Y. and Tanaka, K.: Estimation of energy dissipation in alloys due to stress-induced martensitic transformation. Res Mechanica, 23, 381 (1988).
22. Falk, F.: Pseudoelastic stress-strain curves of polycrystalline shape memory alloys calculated from single crystal data. Int. J. Eng. Sci., 27, 277 (1989).
23. Krasnosel'skii, M. A. and Pokrovskii, A. V.: Systems with Hysteresis, Springer, Berlin, 1989.
24. Liang, C. and Rogers, C. A.: One-dimensional thermomechanical constitutive relations for shape memory materials. J. Intel. Mat. Sys. Struct., 1, 207 (1990).
25. Takagi, T.: A concept of intelligent materials. J. Intel. Mat. Sys. Struct., 1, 149 (1990).
26. Wada, B. K., Fanson, J. L., and Crawley, E. F.: Adaptive structures. J. Intel. Mat. Sys. Struct., 1, 157 (1990).
27. Liang, C. and Rogers, C. A.: The multi-dimensional constitutive relations of shape memory alloys, in Proc. AIAA 32nd Structures, Structural Dynamics and Materials Conference, Baltimore, MD, 1991.
28. Berveiller, M., Pattor, E., and Buisson, M.: Thermomechanical constitutive equations for shape memory alloys. European Symposium on Martensitic Transformation and Shape Memory Properties. J. de Physique IV, 1(C.4), 387 (1991).
29. Huo, Y. Z.: Preisach model for the hysteresis in shape memory alloys, in Proc. of Plasticity '91: The Third International Symposium on Plasticity and Its Current Applications, p. 552, eds., J.-P. Boehler & A. S. Khan, Grenoble, France, 1991.
30. Mayergoyz, I. D.: Mathematical Models of Hysteresis, Springer-Verlag, New York, 1991.
31. Maugin, G. A.: The Thermodynamics of Plasticity and Fracture, Cambridge University Press, New York, 1992.
32. Abeyaratne, R. and Knowles, J. K.: A continuum model of a thermoelastic solid capable of undergoing phase transitions. J. Mech. Phys. Solids, 41, 541 (1993).
33. Brinson, L. C.: One dimensional constitutive behavior of shape memory alloys: Thermodynamical derivation with non-constant material functions. J. Intel. Mat. Sys. Struct., 4(2), 229 (1993).
34. Nemat-Nasser, S. and Hori, M.: Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, Amsterdam, 1993.
35. Sun, Q. P. and Hwang, K. C.: Micromechanics modeling for the constitutive behavior of polycrystalline shape memory alloys - I. Derivation of general relations. J. Mech. Phys. Solids, 41, 1 (1993).
36. Sun, Q. P. and Hwang, K. C.: Micromechanics modeling for the constitutive behavior of polycrystalline shape memory alloys - I. Study of the individual phenomena. J. Mech. Phys. Solids, 41, 19 (1993).
37. Visintin, A., ed.: Models of Hysteresis, Longman Scientific and Technical, New York, 1993.
38. Abeyaratne, R., Chu, C., and James, R. D.: Kinetic and hysteresis in martensitic single crystals, in Mechanics of Phase Transformations and Shape Memory Alloys, Proceedings of the 1994 ASME Winter Annual Meeting, Vol. AMD-189, p. 85, eds., L. C. Brinson & B. Moran, Chicago, 1994.
39. Bo, Z., Kurdila, A. J., Lagoudas, D. C., and Webb, G.: Identification for a class of nonlinear models for SMA embedded elastomeric rods, in Active Materials and Structures, Proceedings of the 31st Annual Meeting of the Society of Engineering Science, Vol. 2427, p. 93, eds., G. L. Anderson & D. C. Lagoudas, College Station, TX, 1994.
40. Escobar, J. C. and Clifton, R. J.: Pressure-shear impact induced phase transformations in Cu-14.44 A1-4.19Ni single crystals, in Active Materials and Structures, Proceedings of the 31st Annual Meeting of the Society of Engineering Science, Vol. 2427, p. 186, eds., G. L. Anderson & D. C. Lagoudas, College Station, TX, 1994.
41. Ivshin, Y. and Pence, T. J., A constitutive model for hysteretic phase transition behavior. Int. J. Eng. Sci., 32(4), 681 (1994).
42. L-models of pseudoelasticity and their specification for some shape memory solids. Eur. J. Mech. A, 13(1), 21 (1994).
43. Bhattacharyya, K. and Kohn, R. V.: Symmetry, texture and the recoverable strain of shape-memory alloy polycrystals. Acta Metall. Mat., 44(2), 529-542 (1995).
44. Hebda, D. A. and White, S. R.: Effect of training conditions and extended thermal cycling on nitinol two-way shape memory behavior. J. Smart Mat. Struct., 4, 298 (1995).
45. Shaw, J. A. and Kyriakides, S.: Thermomechanical aspects of NiTi. J. Mech. Phys. Solids, 43(8), 1243 (1995).
46. Tanaka, K., Nishimura, F., and Tobushi, H.: Transformation start lines in TiNi and Fe-based shape memory alloys after incomplete transformations induced by mechanical and/or thermal loads. Mech. Mat., 19, 271-280 (1995).
47. Boyd, J. and Lagoudas, D. C.: A thermodynamic constitutive model for shape memory materials: Part I. The monolithic shape memory alloy. Part II. The SMA composite material. Int. J. Plasticity, 12(6), 805 (1996).
48. Chopra, I.: Review of current status of smart structures and integrated systems, in Proc. on Smart Structures and Integrated Systems, p. 20, ed., I. Chopra, SPIE, 1996.
49. Culshaw, B.: Smart structures activities worldwide, in Proc. on Smart Structures and Integrated Systems, p. 2, ed., I. Chopra, SPIE, 1996
50. Dickinson, C. A., Hughes, D. C., and Wen, J. T.: Hysteresis in shape memory alloy actuators: The control issues. In Smart Structures and Materials, pp. 494-506, eds., V. V. Varadan, J. Chandra, SPIE 2715, (1996).
51. Lagoudas, D. C. and Bhattacharyya, A.: Modeling of thin layer extensional thermoelectric SMA actuators. (1996).
52. Khachaturyan, A. G.: Theory of Structural Transformation in Solids. John Wiley, New York, 1983.
53. Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. Lon. A, 241, 376-396 (1957).