Shape-memory alloys: Modelling and numerical simulations of the finite-strain superelastic behavior. (English) Zbl 0891.73027
We develop a constitutive model which reproduces the superelastic behavior of shape-memory alloys (SMA) at finite strains. For an isothermal case, we discuss in detail the numerical implementation within a finite element scheme as well as the form of the algorithmically consistent tangent. To assess the viability of the approach, we simulate the response of some simple SMA typical structures (uniaxial test, four-point bending test) as well as an application with possibly a very high impact in different medical fields.
MSC:
| 74B20 | Nonlinear elasticity |
| 74A20 | Theory of constitutive functions in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
uniaxial text; four-point bending test; isothermal case; algorithmically consistent tangentSoftware:
TENSORReferences:
| [1] | Adler, P. H.; Yu, W.; Pelton, A. R.; Zadno, R.; Duerig, T. W.; Barresi, R., On the tensile and torsional properties of pseudoelastic Ni-Ti, Scripta Metall. Mater., 24, 943-947 (1990) |
| [2] | Armero, F.; Simo, J. C., A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity, Int. J. Plastic., 9, 749-782 (1993) · Zbl 0791.73026 |
| [3] | Auricchio, F.; Taylor, R. L.; Lubliner, J., Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior (1996), submitted for publication · Zbl 0898.73019 |
| [4] | Bathe, K. J., Finite Element Procedures in Engineering Analysis (1982), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0528.65053 |
| [5] | Bührer, W.; Zolliker, M.; Gotthardt, R., Crystal structures of the shape memory alloy Ni-Ti, Scripta Metall. Mater., 26, 1149-1151 (1992), (comments on recent publication in Acta Metall. Mater) |
| [6] | Buehler, W. J.; Wiley, R. C., Nickel-based alloys, Technical report (1965), US-Patent 3174851 |
| [7] | Chrysochoos, A.; Lobel, M.; Maisonneuve, O., Thermomechanical coupling of pseudoelastic behaviour of CuZnAl and NiTi alloys, CR Acad. Sci., Ser. II, 320, 217-223 (1995) |
| [8] | Cross, W. B.; Kariotis, A. H.; Stimler, F. J., Technical report, NASA SP 1433 (1969) |
| [9] | (Duerig, T. W.; Melton, K. N.; Stökel, D.; Wayman, C. M., Engineering Aspects of Shape Memory Alloys (1990), Butterworth-Heinemann) |
| [10] | Jackson, C. M.; Wagner, H. J.; Wasilewski, R. J., 55-Nitinol-the alloy with a memory: its physical metallurgy, properties and applications, Technical report, NASA SP 5110 (1972) |
| [11] | Kakeshita, T.; Shimizu, K.; Nakamichi, S.; Tanaka, R.; Endo, S.; Ono, F., Effect of hydrostatic pressures on thermoelastic martensitic transformations in aged Ti-Ni and ausaged Fe-Ni-Co-Ti shape memory alloys, Mater. Trans. JIM, 33, 1-6 (1992) |
| [12] | Khachaturyan, A. G., Theory of Structural Transformations in Solids (1983), John Wiley & Sons |
| [13] | Lee, E. H., Elastic-plastic deformation at finite strains, J. Appl. Mech., 36, 1-6 (1969) · Zbl 0179.55603 |
| [14] | Lubliner, J.; Auricchio, F., Generalized plasticity and shape memory alloys, Int. J. Solids Struct. (1995), in press · Zbl 0902.73034 |
| [15] | Madangopal, K.; Singh, J.; Banerjee, S., The nature of self accommodation in Ni-Ti shape memory alloys, Scripta Metall. Mater., 29, 725-728 (1993) |
| [16] | Maenchen, G.; Sack, S., The tensor code, (Alder, B., Methods in Computational Physics, Vol. 3 (1964), Academic Press), 181 |
| [17] | Mandel, J., Thermodynamics and plasticity, (Dominger, J. J.Delgado; Nina, M. N.R.; Whitelaw, J. H., Foundation of Continuum Thermodynamics (1974)), 283-304 |
| [18] | Melton, K. N., Ni-Ti based shape memory alloys, (Duerig, T. W.; Melton, K. N.; Stökel, D.; Wayman, C. M., Engineering Aspects of Shape Memory Alloys (1990)), 21-35 |
| [19] | Melzer, A.; Stökel, D., Performance improvement of surgical instrumentation through the use of Ni-Ti materials, (Pelton, A. R.; Hodgson, D.; Duerig, T., Proc. First International Conference on Shape Memory and Superelastic Technologies (1994)), 401-409 |
| [20] | Miyazaki, S.; Otsuka, K.; Wayman, C. M., The shape memory mechanism associated with the martensitic transformation in Ti-Ni alloys—I. Self-accommodation, Acta Metall., 37, 1873-1884 (1989) |
| [21] | Miyazaki, S.; Otsuka, K.; Wayman, C. M., The shape memory mechanism associated with the martensitic transformation in Ti-Ni alloys—II. Variant coalescence and shape recovery, Acta Metall., 37, 1885-1890 (1989) |
| [22] | Simo, J. C., Topics on the numerical analysis and simulation of plasticity, (Ciarlet, P. G.; Lions, J. L., Handbook of Numerical Analysis, Vol. III (1996), Elsevier Science Publisher B.V), in press · Zbl 0930.74001 |
| [23] | Simo, J. C., Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Engrg., 99, 61-112 (1992) · Zbl 0764.73089 |
| [24] | Simo, J. C.; Hughes, T. J.R., Elasto-plasticity and Visco-plasticity: Computational Aspects (1996), Springer-Verlag, in press |
| [25] | Tamura, I.; Wayman, C. M., Martensitic transformations and mechanical effects, (Olson, G. B.; Owen, W. S., Martensite: A Tribute to Morris Cohen (1992)), 227-242 |
| [26] | Wang, F. E., (Proceeding of symposium of NiTi and related compounds. Technical report. Proceeding of symposium of NiTi and related compounds. Technical report, NOLTR 68-16 (1968)) |
| [27] | Wayman, C. M., Introduction to the Crystallography of Martensitic Transformations (1964), MacMillan |
| [28] | Wick, A., The bending behavior of superelastic NiTi, (Master’s thesis (1994), Universität Karlsruhe (TH), Institut für Werkstoffkunde I) |
| [29] | Wilkins, M. L., Calculation of elastic plastic flow, (Alder, B., Methods in Computational Physics, Vol. 3 (1964), Academic Press), 211 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
