The Research of the Difference between Small-Strain and Large-Strain Formulations for Shape Memory Alloys

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Based on thermodynamics and phase transformation driving force, we apply a SMA constitutive model to analyze the large and small deformation of SMA materials. Simulations under different loading, uniaxial tension and shear conditions, illustrate the characteristics of the model in large strain deformation and small strain deformation. The results indicate that the difference between the two methods is small under the uniaxial tension case, while the large deformation and the small deformation results are very different under shear deformation case. It lays a foundation for the further studies of the constitutive model of SMA, especially in the multiaxial non-proportional loading aspects.

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Edited by:

Mohamed Othman

Pages:

3-9

Citation:

J. Yao et al., "The Research of the Difference between Small-Strain and Large-Strain Formulations for Shape Memory Alloys", Applied Mechanics and Materials, Vols. 229-231, pp. 3-9, 2012

Online since:

November 2012

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$38.00

[1] Lagoudas DC,Entchev PB. Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: Constitutive model for fully dense SMAs[J]. Mechanics of Materials. 2004, 36: 865-896.

DOI: https://doi.org/10.1016/j.mechmat.2003.08.006

[2] Lagoudas DC,Entchev PB et al. Shape memory alloys, Part II: Modeling of polycrystals[J]. Mechanics of Materials, 2006, 38(5-6): 430-462.

DOI: https://doi.org/10.1016/j.mechmat.2005.08.003

[3] Lexcellent C, Leclerq S, Gabry B, Bourbon G. The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological mode Interational[J]. Journal of Plasticity, 2000, 16: 1155-1168.

DOI: https://doi.org/10.1016/s0749-6419(00)00005-x

[4] Boubakar. ML, Moyne S, Lexcellent C. SMA pseudoelastic finite strains:theroy and numerical application[J]. Journal of Engineering Materials and Technology. 1999, 121: 44-45.

DOI: https://doi.org/10.1115/1.2815998

[5] Moyne S,Boubakar ML,Lexcellent C. Extension of a Linear Behaviour Model of Shape Memory Alloys for Finite Strain Studies[J] Journal of physics, 1997 5:83-88.

DOI: https://doi.org/10.1051/jp4:1997513

[6] Lexellent C, Boubakar ML, Bouvet C, Calloch S. About modeling the shape memory alloy behaviour based on the phase transformation surface identification under proportional loading and anisothermal conditions[J]. International Journal of Solids and Structures, 2006, 43: 613-626.

DOI: https://doi.org/10.1016/j.ijsolstr.2005.07.004

[7] Qidwai MA, Lagoudas DC. On thermomechanics and transformation surfaces of poly-crystalline NiTi shape memory alloy material[J]. Interational Journal of Plasticity, 2000, 16: 1309-1343.

DOI: https://doi.org/10.1016/s0749-6419(00)00012-7

[8] Auricchio F, Taylor RL. Shape-memory alloys: modeling and numerical simulations of the finite-strain superelastic behavior[J]. Computer Methods in Applied Mechanics and Engineering. 1997, 143: 175-194.

DOI: https://doi.org/10.1016/s0045-7825(96)01147-4

[9] Auricchio F, Taylor RL. Lublincr J. Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior[J]. Computer Methods in Applied Mechanics and Engineering. 1997, 146: 281-312.

DOI: https://doi.org/10.1016/s0045-7825(96)01232-7

[10] Auricchio F. A robust integrationalorithm for a finite-strain shape memory alloy superelastic model[J]. International Journal of Plasticity. 2001, 17: 971-990.

DOI: https://doi.org/10.1016/s0749-6419(00)00050-4

[11] Auricchio F, Beirão L, DaVeiga, Lovadina C, Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199: 314-323.

DOI: https://doi.org/10.1016/j.cma.2008.06.004

[12] Helm,Stress computation in finite thermoviscoplasticity[J], International Journal of Plasticity, 2006, 22: 1699-1727.

DOI: https://doi.org/10.1016/j.ijplas.2006.02.007

[13] Helm D, Haupt P. Shape memory behaviour: modelling within continuum thermomechanics[J]. International Journal of solids and Structures, 2003, 40: 827-849.

DOI: https://doi.org/10.1016/s0020-7683(02)00621-2

[14] Christ D, Reese S. Finite element modeling of shape memory alloys-A comparison between small-strain and large-strain formulations[J]. Materials Science and Engineering A, 2008, 481-482: 343-346.

DOI: https://doi.org/10.1016/j.msea.2006.11.174

[15] Reese S, Christ D. Finite deformation pseudoelasticity of shape memory alloys Constitutive modeling and finite element implementation[J]. International Journal of Plasticity. 2008, 24: 455-482.

DOI: https://doi.org/10.1016/j.ijplas.2007.05.005

[16] Christ D, Reese S A finite element model for shape memory alloys considering thermomechanial couplings at large strains[J]. International Journal of solids and Structures. 2009, 46: 3694-3709.

DOI: https://doi.org/10.1016/j.ijsolstr.2009.06.017

[17] Raniecki B, Lexcellent C, Tanaka K. Thermodynamic models of pseudoelastic behaviour of shape memory alloys[J]. Archives of Mechanics. 1992, 44(3): 261-284.

[18] Tanakz K A phenomenological description on thermomechanical behavior of shape memory alloys[J]. International Journal of Pressure Vessels and technology. 1990, 112: 158-163.

DOI: https://doi.org/10.1115/1.2928602

[19] Zhu Yuping, Some Studies on Constitutive Model of Shape Memory Alloy[D]. p.12(in Chinese).