×

A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties. (English) Zbl 1227.74037

Summary: The research toward an exhaustive modeling of the macroscopic behavior of shape memory alloys (SMAs) has been widely growing in last years because of the increasing employment of such smart materials in a large number of applications in many fields of engineering. Within this context, it has to be remarked that many models for SMAs available in the literature are able to properly reproduce main macroscopic SMA behaviors (i.e., superelasticity and shape-memory effect), without however modeling secondary effects that may turn out to be relevant in some practical cases. In this paper, we propose a new phenomenological one-dimensional model, which takes into account tension-compression asymmetries as well as elastic properties depending on the phase transformation level, combined with a good description of the superelastic and shape-memory behaviors. Moreover, we present some numerical tests showing model features and performance.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74N05 Crystals in solids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Auricchio, F.; Sacco, E., A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite, Int. J. Non-Linear Mech., 32, 1101-1114 (1997) · Zbl 0906.73006
[2] Auricchio, F.; Petrini, L., A three-dimensional model describing stress-temperature induced solid phase transformations. Part I: Solution algorithm and boundary value problems, Int. J. Numer. Methods Engrg., 61, 807-836 (2004) · Zbl 1075.74599
[3] Auricchio, F.; Reali, A., A phenomenological one-dimensional model describing stress-induced solid phase transformation with permanent inelasticity, Mech. Adv. Mater. Struct., 14, 43-55 (2007) · Zbl 1105.74031
[4] Auricchio, F.; Reali, A.; Stefanelli, U., A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity, Int. J. Plast., 23, 207-226 (2007) · Zbl 1105.74031
[5] (Duerig, T. W.; Melton, K. N.; Stökel, D.; Wayman, C. M., Engineering Aspects of Shape Memory Alloys (1990), Butterworth-Heinemann)
[6] T.W. Duerig, A.R. Pelton (Eds.), SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference, ASM International, 2003.; T.W. Duerig, A.R. Pelton (Eds.), SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference, ASM International, 2003.
[7] Govindjee, S.; Miehe, C., A multi-variant martensitic phase transformation model: formulation and numerical implementation, Comput. Methods Appl. Mech. Engrg., 191, 215-238 (2001) · Zbl 1007.74061
[8] Helm, D.; Haupt, P., Shape memory behaviour: modelling within continuum thermomechanics, Int. J. Solids Struct., 40, 827-849 (2003) · Zbl 1025.74022
[9] Lagoudas, D. C.; Entchev, P. B.; Popov, P.; Patoor, E.; Brinson, L. C.; Gao, X., Shape memory alloys, Part II: Modeling of polycrystals, Mech. Mater., 38, 391-429 (2006)
[10] Popov, P.; Lagoudas, D. C., A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite, Int. J. Plast., 23, 1679-1720 (2007) · Zbl 1127.74008
[11] Levitas, V. I., Thermomechanical theory of martensitic phase transformations in inelastic materials, Int. J. Solids Struct., 35, 889-940 (1998) · Zbl 0931.74059
[12] Peultier, B.; Ben Zineb, T.; Patoor, E., Macroscopic constitutive law for SMA: application to structure analysis by FEM, Mater. Sci. Engrg.: A, 438-440, 454-458 (2006)
[13] Peigney, M., A time-integration scheme for thermomechanical evolutions of shape-memory alloys, Comput. Rend. Mech., 334, 266-271 (2006) · Zbl 1343.74049
[14] Raniecki, B.; Lexcellent, Ch., \(R_L\) models of pseudoelasticity and their specification for some shape-memory solids, Eur. J. Mech., A: Solids, 13, 21-50 (1994) · Zbl 0795.73010
[15] Reese, S.; Christ, D., Finite deformation pseudo-elasticity of shape memory alloys – constitutive modelling and finite element implementation, Int. J. Plast. (2007)
[16] Souza, A. C.; Mamiya, E. N.; Zouain, N., Three-dimensional model for solids undergoing stress-induced phase transformations, Eur. J. Mech., A: Solids, 17, 789-806 (1998) · Zbl 0921.73024
[17] Simo, J. C.; Hughes, T. J.R., Computational Inelasticity (1998), Springer-Verlag · Zbl 0934.74003
[18] Stein, E.; Zwickert, O., Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains, Comput. Mech., 40, 429-445 (2007) · Zbl 1160.74036
[19] Thamburaja, P.; Anand, L., Polycrystalline shape-memory materials: effect of crystallographic texture, J. Mech. Phys. Solids, 49, 709-737 (2001) · Zbl 1011.74049
[20] Thiebaud, F.; Lexcellent, Ch.; Collet, M.; Foltete, E., Implementation of a model taking into account the asymmetry between tension and compression, the temperature effects in a finite element code for shape memory alloys structures calculations, Comput. Mater. Sci. (2007)
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.