D. Bernardini, On the macroscopic free energy functions for shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.49, issue.4, pp.813-837, 2001.
DOI : 10.1016/S0022-5096(00)00050-8

D. Bernardini and T. Pence, Uniaxial Modeling of Multivariant Shape-Memory Materials with Internal Sublooping using Dissipation Functions, Meccanica, vol.9, issue.4-6, pp.339-364, 2005.
DOI : 10.1007/s11012-005-2103-4

D. Bernardini and G. Rega, The influence of model parameters and of the thermomechanical coupling on the behavior of shape memory devices, International Journal of Non-Linear Mechanics, vol.45, issue.10, pp.933-946, 2009.
DOI : 10.1016/j.ijnonlinmec.2009.11.019

D. Bernardini and F. Vestroni, Non-isothermal oscillations of pseudoelastic devices, International Journal of Non-Linear Mechanics, vol.38, issue.9, pp.1297-1313, 2003.
DOI : 10.1016/S0020-7462(02)00065-3

A. Chrysochoos, H. Pham, and O. Maisonneuve, Energy balance of thermoelastic martensite transformation under stress, Nuclear Engineering and Design, vol.162, issue.1, pp.1-2, 1996.
DOI : 10.1016/0029-5493(95)01140-4

M. Collet, E. Folte?tefolte?te, and C. Lexcellent, Analysis of the behavior of a Shape Memory Alloy beam under dynamical loading, European Journal of Mechanics - A/Solids, vol.20, issue.4, pp.615-630, 2001.
DOI : 10.1016/S0997-7538(01)01159-7

S. A. Doare´odoare´o and . Touze´ctouze´c, Experimental analysis of the quasi-static and dynamic torsional behaviour of shape memory alloys, International Journal of Solids and Structures, vol.49, issue.1, pp.32-42, 2011.
DOI : 10.1016/j.ijsolstr.2011.09.009

Z. Feng and D. Li, Dynamics of a Mechanical System with a Shape Memory Alloy Bar, Journal of Intelligent Material Systems and Structures, vol.4, issue.4, pp.399-410, 1996.
DOI : 10.1177/1045389X9600700404

H. Funakubo, Shape Memory Alloys, Precision Machinery and Robotics, vol.1, 1987.

M. Ge´radinge´radin and D. Rixen, Mechanical Vibrations: Theory and Application to Structural Dynamics, 1994.

C. Grabe and O. Bruhns, On the viscous and strain rate dependent behavior of polycrystalline NiTi, International Journal of Solids and Structures, vol.45, issue.7-8, pp.7-8, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.029

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983.

D. Hartl, J. Mooney, and D. Lagoudas, Use of a Ni60Ti shape memory alloy for active jet engine chevron application: I. Thermomechanical characterization, Smart Materials and Structures, vol.19, issue.1, p.15020, 2010.
DOI : 10.1088/0964-1726/19/1/015020

Y. He and Q. Sun, On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars, International Journal of Solids and Structures, vol.48, issue.11-12, pp.1688-1695, 2011.
DOI : 10.1016/j.ijsolstr.2011.02.017

URL : https://hal.archives-ouvertes.fr/hal-00830703

O. Helm and P. Haupt, Thermomechanical representation of the multiaxial behavior of shape memory alloys, Proceedings of SPIE: Smart Structure and Materials 2002: Active Materials: Behavior and Mechanics, pp.343-354, 2002.

T. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, 2000.

J. Humbeeck and L. Delaey, The influence of strainrate , amplitude and temperature on the hysteresis of a pseudoelastic Cu-Zn-Al single crystal, Journal de Physique IV, vol.42, pp.1007-1011, 1981.
URL : https://hal.archives-ouvertes.fr/jpa-00221028

W. Lacarbonara, D. Bernardini, and F. Vestroni, Nonlinear thermomechanical oscillations of shape-memory devices, International Journal of Solids and Structures, vol.41, issue.5-6, pp.1209-1234, 2004.
DOI : 10.1016/j.ijsolstr.2003.10.015

D. Lagoudas, L. Machado, and M. Lagoudas, Nonlinear vibration of a one-degree of freedom shape memory alloy oscillator: a numerical-experimental investigation. In: Structural dynamics and materials conference, pp.18-22, 2005.

P. Leo, T. Shield, and O. Bruno, Transient heat transfer effects on the pseudoelastic behavior of shape-memory wires, Acta Metallurgica et Materialia, vol.41, issue.8, pp.2477-2485, 1993.
DOI : 10.1016/0956-7151(93)90328-P

C. Lexcellent and J. Rejzner, Modeling of the strain rate effect, creep and relaxation of a Ni-Ti shape memory alloy under tension (compression) - torsional proportional loading in the pseudoelastic range, Smart Materials and Structures, vol.9, issue.5, pp.613-621, 2000.
DOI : 10.1088/0964-1726/9/5/305

P. Lin, H. Tobushi, and K. Tanaka, Influence of Strain Rate on Deformation Properties of TiNi Shape Memory Alloy., Transactions of the Japan Society of Mechanical Engineers Series A, vol.60, issue.576, pp.117-123, 1996.
DOI : 10.1299/kikaia.60.1837

L. Machado, D. Lagoudas, and M. Savi, Lyapunov exponents estimation for hysteretic systems, International Journal of Solids and Structures, vol.46, issue.6, pp.1269-1286, 2009.
DOI : 10.1016/j.ijsolstr.2008.09.013

L. Machado, M. Savi, and P. Pacheco, Nonlinear dynamics and chaos in coupled shape memory oscillators, International Journal of Solids and Structures, vol.40, issue.19, pp.5139-5156, 2003.
DOI : 10.1016/S0020-7683(03)00260-9

P. Manneville, Dissipative structures and weak turbulence, 1990.
DOI : 10.1007/3-540-60188-0_59

C. Morin, Z. Moumni, and W. Zaki, A constitutive model for shape memory alloys accounting for thermomechanical coupling, International Journal of Plasticity, vol.27, issue.5, pp.748-767, 2011.
DOI : 10.1016/j.ijplas.2010.09.005

Z. Moumni, Sur la mode´lisation du changement de phase a` l e´tat solide, 1995.

Z. Moumni, W. Zaki, and Q. Nguyen, Theoretical and numerical modeling of solid???solid phase change: Application to the description of the thermomechanical behavior of shape memory alloys, International Journal of Plasticity, vol.24, issue.4, pp.614-645, 2008.
DOI : 10.1016/j.ijplas.2007.07.007

K. Mukherjee, S. Sircar, and N. Dahotre, Thermal effects associated with stress-induced martensitic transformation in a Ti???Ni alloy, Materials Science and Engineering, vol.74, issue.1, pp.75-84, 1985.
DOI : 10.1016/0025-5416(85)90111-9

S. Nemat-nasser, W. , and G. , Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures, Mechanics of Materials, vol.38, issue.5-6, pp.5-6, 2006.
DOI : 10.1016/j.mechmat.2005.07.004

L. Orgeás and D. Favier, Stress-induced martensitic transformation of a NiTi alloy in isothermal shear, tension and compression, Acta Materialia, vol.46, issue.15, pp.5579-5591, 1998.
DOI : 10.1016/S1359-6454(98)00167-0

U. Parlitz and W. Lauterborn, Superstructure in the bifurcation set of the Duffing equation, Physics Letters A, vol.107, issue.8, pp.351-355, 1985.
DOI : 10.1016/0375-9601(85)90687-5

E. Patoor and M. Berveiller, Les Alliages a` Me´moire de Forme, 1990.

M. Qidwai and D. Lagoudas, On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material, International Journal of Plasticity, vol.16, issue.10-11, pp.1309-1343, 2000.
DOI : 10.1016/S0749-6419(00)00012-7

S. Saadat, J. Salichs, and M. Noori, An overview of vibration and seismic applications of NiTi shape memory alloy, Smart Materials and Structures, vol.11, issue.2, pp.218-229, 2002.
DOI : 10.1088/0964-1726/11/2/305

M. Savi and P. Pacheco, CHAOS AND HYPERCHAOS IN SHAPE MEMORY SYSTEMS, International Journal of Bifurcation and Chaos, vol.12, issue.03, pp.645-657, 2002.
DOI : 10.1142/S0218127402004607

M. Savi, P. Pacheco, and A. Braga, Chaos in a shape memory two-bar truss, International Journal of Non-Linear Mechanics, vol.37, issue.8, pp.1387-1395, 2002.
DOI : 10.1016/S0020-7462(02)00029-X

M. Savi, M. Sa, and A. Paiva, Tensile-compressive asymmetry influence on shape memory alloy system dynamics, Chaos, Solitons & Fractals, vol.36, issue.4, pp.828-842, 2008.
DOI : 10.1016/j.chaos.2006.09.043

A. Sbarra, . Doare´odoare´o, and M. Moussa, Dynamical behaviour of a shape memory alloy torsional pendulum, Proceedings of ENOC 2011, pp.24-29, 2011.

I. Schmidt and R. Lammering, The damping behaviour of superelastic NiTi components, Materials Science and Engineering: A, vol.378, issue.1-2, pp.70-75, 2004.
DOI : 10.1016/j.msea.2003.09.106

H. Schuster and W. Just, Deterministic Chaos: An Introduction, 2005.
DOI : 10.1002/3527604804

S. Seelecke, Modeling the dynamic behavior of shape memory alloys, International Journal of Non-Linear Mechanics, vol.37, issue.8, pp.1363-1374, 2002.
DOI : 10.1016/S0020-7462(02)00030-6

J. Shaw and S. Kyriakides, Thermomechanical aspects of NiTi, Journal of the Mechanics and Physics of Solids, vol.43, issue.8, pp.1243-1281, 1995.
DOI : 10.1016/0022-5096(95)00024-D

E. Sitnikova, E. Pavlovskaia, and M. Wiercigroch, Dynamics of an impact oscillator with SMA constraint, The European Physical Journal Special Topics, vol.165, issue.1, pp.1269-1286, 2008.
DOI : 10.1140/epjst/e2008-00866-8

E. Sitnikova, E. Pavlovskaia, and M. Wiercigroch, Vibration reduction of the impact system by an SMA restraint: numerical studies, International Journal of Non-Linear Mechanics, vol.45, issue.9, pp.837-849, 2010.
DOI : 10.1016/j.ijnonlinmec.2009.11.013

W. Zaki, An approach to modeling tensile???compressive asymmetry for martensitic shape memory alloys, Smart Materials and Structures, vol.19, issue.2, p.25009, 2007.
DOI : 10.1088/0964-1726/19/2/025009

W. Zaki and Z. Moumni, A 3D model of the cyclic thermomechanical behavior of shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.55, issue.11, pp.2427-2454, 2007.
DOI : 10.1016/j.jmps.2007.03.011

W. Zaki and Z. Moumni, A three-dimensional model of the thermomechanical behavior of shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.55, issue.11, pp.2455-2490, 2007.
DOI : 10.1016/j.jmps.2007.03.012

W. Zaki, S. Zamfir, and Z. Moumni, An extension of the ZM model for shape memory alloys accounting for plastic deformation, Mechanics of Materials, vol.42, issue.3, pp.266-274, 2010.
DOI : 10.1016/j.mechmat.2009.11.013