A finite-strain finite element model for the pseudoelastic behavior of shape memory alloys

Computer Methods in Applied Mechanics and Engineering

Volumn 148, Issue 1-2, 1997, Pages 23-37

  Masud, Arif ^a   Panahandeh, Mohammad ^b   Aurrichio, Ferdinando ^c,d  

^a 1120 Science and Engineering Offices   (United States)

^b Berkeley Appl Sci and Engineering   (United States)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

^d Berkeley   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOYS; COMPUTER SIMULATION; DEFORMATION; FINITE ELEMENT METHOD; LOADS (FORCES); MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PHASE TRANSITIONS; PLASTICITY; SHAPE MEMORY EFFECT; STRAIN; THERMAL EFFECTS;

CONSTITUTIVE EQUATIONS; FINITE ELEMENT MODEL; HENCKY STRAIN; NEWTON-RAPHSON ITERATION SCHEME; SHAPE MEMORY ALLOYS;

ELASTICITY;

EID: 0031209666     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00080-7     Document Type: Article

References (41)

1. R. Abeyaratne and J.K. Knowles, A continuum model of thermoelastic solid capable of undergoing phase transitions, J. Mech. Phys. Solids 41 (1993) 541-571.
2. D. Brandon and R.C. Rogers, Constitutive laws for pseudo-elastic materials, J. Intell. Mater. Syst. Struct. 3 (1992) 255-267.
3. L.C. Brinson, One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variables, J. Intell. Mater. Syst. Struct. 4 (1993) 229-242.
4. L.C. Brinson, A. Bekker and S. Hwang, Deformation of shape memory alloys due to thermo-induced transformations, J. Intell. Mater. Syst. Struct., to appear.
5. L.C. Brinson and S. Hwang, Simplifications and comparisons of shape memory alloy constitutive models, J. Intell. Mater. Syst. Struct., to appear.
6. L.C. Brinson and R. Lammering, Finite element analysis of the behavior of shape memory alloys and their applications, J. Intell. Mater. Syst. Struct. 30(23) (1993) 3261-3280.
7. J.S. Cory and J.R. McNichols Jr., Nonequilibrium thermostatics, J. Appl. Phys. 58 (1985) 3282-3294.
8. A. Cuitino and M. Ortiz, A material-independent method for extending stress plasticity to finite plasticity with multiplicative kinematics, Engrg. Comput. 9 (1992) 437-451.
9. L. Delaey, R.V. Krishnan, H. Tas and H. Warlimont, Review - thermoelasticity, pseudoelasticity and the memory effects associated with martensitic transformations - Part 2. The macroscopic mechanical behavior, J. Mater. Sci. 9 (1974) 1536-1544.
10. A.L. Eterovic and K.J. Bathe, A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures. Int. J. Numer. Methods Engrg. 30 (1990) 1099-1114.
11. F. Falk and P. Konopka, Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys, J. Phys.: Cond. Mat. 2 (1990) 61-77.
12. S. Fu, I. Muller and H. Xu, The interior of pseudoelastic hysteresis, Mater. Res. Soc, Symp. Proc. (1992) 246.
13. S. Fu, M. Huo and I. Muller, Thermodynamics of pseudoelasticity - an analytical approach, Acta Mech. 99 (1993) 1-19.
14. H. Funakubo, Shape Memory Alloys (translated from the Japanese by J.B. Kennedy) (Gordon and Breach Science Publishers, New York, 1987).
15. T.J.R. Hughes, The finite element method: linear static and dynamic finite element analysis (Prentice-Hall, Englewood Cliffs, NJ, 1987).
16. T.J.R. Hughes and K. Pister, Consistent linearization in mechanics of solids and structures, Comput. Struct. 8 (1978) 391-397.
17. Y. Huo and I. Muller. Nonequilibrium thermodynamics of pseudoelasticity, Cont. Mech. Thermodyn. (1993).
18. Y. Ivshin and J. Pence, A constitutive model for hysteretic phase transition behavior, Int. J. Engrg. Sci. 32 (1994) 681-704.
19. C. Liang and C.A. Rogers, One-dimensional thermomechanical constitutive relations for shape memory materials, J. Intell. Mater. Syst. Struct. 1 (1990) 207-234.
20. C. Liang and C.A. Rogers, A multi-dimensional constitutive model for shape memory alloys, J. Engrg, Mech. 26 (1992) 429-443.
21. J. Lubliner, Plasticity Theory (Macmillan Publishing Company, New York, 1993).
22. J.E. Marsen and T.J.R. Hughes, Mathematical foundations of elasticity (Dover Publishing Inc., New York, 1983).
23. B. Moran, M. Ortiz and C.F. Shih, Formulation of implicit finite element methods for multiplicative finite deformation plasticity, Int. J. Numer. Methods Engrg. 29 (1990) 483-514.
24. I. Muller and H. Xu, On the pseudo-elastic hysteresis, Acta Metall. Mater. 39 (1991) 263-271.
25. M. Ortiz and J.C. Simo, An analysis of a new class of integration algorithms for elastoplastic constitutive relations, Int. J. Numer. Methods Engrg. 23 (1986) 353-366.
26. E. Patoor, A. Eberhardt and Berveiller, Thermomechanical behavior of shape memory alloys, Archiv. Mech. 40 (1988) 755-794.
27. J. Perkins, G.R. Edwards, C.R. Such, J.M. Johnson and R.R. Allen, Thermomechanical characteristics of alloys exhibiting martensitic thermoelasticity, in: J. Perkins, ed., Shape Memory Effects in Alloys (Plenum Press, New York, 1976).
28. J.C. Simo, Variational and projection methods for the volume constraint in finite deformation elastoplasticity, Comput. Methods Appl. Mech. Engrg. 51 (1985) 177-208.
29. J.C. Simo, A framework for finite strain elastoplasticity based on maximum plastic dissipation and multiplicative decomposition: Part I. Continuum formulation; Part II. Computational aspects, Comput. Methods Appl. Mech. Engrg. 66 (1988a) 199-219 and 68 (1988b) 1-31.
30. J.C. Simo, A framework for finite strain elastoplasticity based on maximum plastic dissipation and multiplicative decomposition: Part I. Continuum formulation; Part II. Computational aspects, Comput. Methods Appl. Mech. Engrg. 66 (1988a) 199-219 and 68 (1988b) 1-31.
31. J.C. Simo, Topics on the numerical analysis and simulation of plasticity, in: P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis, Vol. III (Elsevier Science Publishers B.V., North Holland, 1995).
32. J.C, Simo and F. Armero, Recent advances in the formulation and numerical analysis of thermoplasticity at finite strains, in: D. Besdo and E. Stein, eds., Finite Inelastic Deformations: Theory and Applications, IUTAM Symposium, Hannover, 1991 (Springer Verlag, Berlin, 1992).
33. J.C. Simo and T.J.R. Hughes, Elasto-plasticity and Visco-plasticity: Computational Aspects (Springer-Verlag, 1993).
34. J.C. Simo and M. Ortiz, A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations, Comput. Methods Appl. Mech. Engrg. 49 (1985) 221-245.
35. J.C. Simo and R.L. Taylor, Consistent tangent operators for rate independent elastoplasticity, Comput. Methods Appl. Mech. Engrg. 48 (1985) 101-118.
36. K. Tanaka, A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior, Res. Mech. 18 (1986) 251-263.
37. K. Tanaka, T. Hayashi, T. Itoh and H. Tobushi, Analysis of thermomechanical behavior of shape memory alloys, Mech. Mater. 13 (1992) 207-215.
38. K. Tanaka, S. Kobayashi and Y. Sato, Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys, Int. J. Plasticity 2 (1986) 59-72.
39. H. Tobushi, H. Iwanaga, H. Tanaka, T. Hori and T. Sawada, Deformation behavior of TiNi shape memory alloy subjected to variable stress and temperature, Cont. Mech. Thermodyn. 3 (1991) 79-93.
40. C.M. Wayman and T.W. Duerig, An introduction to martensite and shape memory, in: T.W. Duerig, K.N. Melton, D. Stockel and C.M. Wayman, eds., Engineering Aspects of Shape Alloys (Butterworth-Heinemann, Boston, 1990) 3-20.
41. K. Wilmanski, Symmetric model of stress-strain hysteresis loops in shape memory alloys, Int. J. Engrg. Sci. 31 (1993) 1121-1138.