K. M. Armattoe, M. Haboussi, and T. Ben-zineb, A 2D nite element based on a nonlocal constitutive model describing localization and propagation of phase transformation in shape memory alloy thin structures, International Journal of Solids and Structures, vol.51, issue.6, pp.1208-1220, 2014.

A. Barnoush, Hydrogen Embrittlement, Revisited by in Situ Electrochemical Nanoindentation. Saarbrücker Reihe Materialwissenschaft und Werkstotechnik. Shaker, 2009.

L. Bataillard, Transformation martensitique multiple dans un alliage à mémoire de forme Ni-Ti, 1996.

H. K. Birnbaum and P. Sofronis, Hydrogen enhanced localized plasticity a mechanism for hydrogenrelated fracture, Materials Science and Engineering : A, vol.176, issue.1-2, p.191202, 1994.

A. Biscarini, R. Campanella, B. Coluzzi, G. Mazzolai, L. Trotta et al., Martensitic transitions and mechanical spectroscopy of Ni 50.8 Ti 49.2 alloy containing hydrogen, Acta Materialia, vol.47, issue.18, p.45254533, 1999.

F. C. Borges and F. M. Fernandes, Iron Based Shape Memory Alloys : Mechanical and Structural Properties, 2013.

C. Bouvet, S. Calloch, and C. Lexcellent, A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings, European Journal of Mechanics-A/Solids, vol.23, issue.1, p.3761, 2004.

J. G. Boyd and D. C. Lagoudas, A thermodynamical constitutive model for shape memory materials. part I. the monolithic shape memory alloy, International Journal of Plasticity, vol.12, issue.6, p.805842, 1996.

J. G. Boyd and D. C. Lagoudas, A thermodynamical constitutive model for shape memory materials. part II. the SMA composite material, International Journal of Plasticity, vol.12, issue.7, p.843873, 1996.

Y. Chemisky, Modélisation du comportement macroscopique des alliages à mémoire de forme : application aux matériaux composites, 2009.

Y. Chemisky, A. Duval, E. Patoor, and T. Ben-zineb, Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation, Mechanics of Materials, vol.43, issue.7, p.361376, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01769302

C. Q. Chen, S. X. Li, and K. Lu, The deformation behaviors of gamma hydrides in titanium under cyclic straining, Acta materialia, vol.51, issue.4, p.931942, 2003.

C. Q. Chen, S. X. Li, H. Zheng, L. B. Wang, and K. Lu, An investigation on structure, deformation and fracture of hydrides in titanium with a large range of hydrogen contents, Acta materialia, vol.52, issue.12, p.36973706, 2004.

F. T. Cheng, P. Shi, and H. C. Man, Eect of electrolytic hydrogen pre-charging on the cavitation erosion resistance of NiTi : a preliminary study, Scripta materialia, vol.47, issue.2, pp.89-94, 2002.

P. Chowdhury, L. Patriarca, G. Ren, and H. Sehitoglu, Molecular dynamics modeling of niti superelasticity in presence of nanoprecipitates, International Journal of Plasticity, vol.81, p.152167, 2016.

B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Archive for Rational Mechanics and Analysis, vol.13, p.167178, 1963.

A. Cottrell, An Introduction to Metallurgy, 1975.

J. Crank, The mathematics of diusion, 1979.

R. Dasgupta, A look into cu-based shape memory alloys : Present scenario and future prospects, Journal of Materials Research, vol.29, issue.16, p.16811698, 2014.

G. N. Dayananda and M. S. Rao, Eect of strain rate on properties of superelastic NiTi thin wires, Materials Science and Engineering : A, vol.486, issue.1, p.96103, 2008.

C. , D. Leo, and L. Anand, Hydrogen in metals : A coupled theory for species diusion and large elasticplastic deformations, International Journal of Plasticity, vol.43, p.4269, 2013.

A. Diaz, J. M. Alegre, and I. I. Cuesta, A review on diusion modelling in hydrogen related failures of metals, Engineering Failure Analysis, vol.66, p.577595, 2016.

T. W. Duerig, A. Pelton, and D. Stöckel, An overview of nitinol medical applications, Materials Science and Engineering : A, vol.273, p.149160, 1999.
DOI : 10.1016/s0921-5093(99)00294-4

A. Duval, Modélisation du comportement thermomécanique d'alliages à mémoire de forme. Application au dimensionnement de microsystèmes et extension en non local, 2009.

A. Duval, Modélisation du comportement thermomécanique dálliages à mémoire de forme. Application au dimensionnement de microsystèmes et extension en non local, 2010.

M. Es-souni, M. Es-souni, and H. Fischer-brandies, Assessing the biocompatibility of NiTi shape memory alloys used for medical applications, Analytical and Bioanalytical Chemistry, vol.381, issue.3, p.557567, 2005.

Y. Fukai, The metalhydrogen system : basic bulk properties, vol.21, 2006.

F. Gamaoun and T. Hassine, Ageing eect and rate dependency of a NiTi shape memory alloy after hydrogen charging, Journal of Alloys and Compounds, vol.615, pp.680-683, 2014.
DOI : 10.1016/j.jallcom.2013.10.214

F. Gamaoun, M. Ltaief, T. Bouraoui, and T. Ben-zineb, Eect of hydrogen on the tensile strength of aged NiTi superelastic alloy, Journal of Intelligent Material Systems and Structures, vol.22, issue.17, p.20532059, 2011.

A. N. Gorban, H. P. Sargsyan, and H. A. Wahab, Quasichemical models of multicomponent nonlinear diusion, Mathematical Modelling of Natural Phenomena, vol.6, issue.5, p.184262, 2011.
DOI : 10.1051/mmnp/20116509

URL : https://www.mmnp-journal.org/articles/mmnp/pdf/2011/05/mmnp201165p184.pdf

G. Guillonneau, Nouvelles techniques de nano-indentation pour des conditions expérimen-tales diciles : très faibles enfoncements, surfaces rugueuses, température, 2012.

M. E. Gurtin, E. Fried, and L. Anand, The mechanics and thermodynamics of continua, 2010.
DOI : 10.1017/cbo9780511762956

E. F. Harris, S. M. Newman, and J. A. Nicholson, Nitinol arch wire in a simulated oral environment. Changes in mechanical properties, American Journal of Orthodontics and Dentofacial Orthopedics, vol.93, issue.6, p.508513, 1988.

D. J. Hartl and D. C. Lagoudas, Aerospace applications of shape memory alloys, Proceedings of the Institution of Mechanical Engineers, vol.221, p.535552, 2007.
DOI : 10.1243/09544100jaero211

URL : https://journals.sagepub.com/doi/pdf/10.1243/09544100JAERO211

J. Y. He, K. W. Gao, Y. J. Su, L. J. Qiao, and W. Y. Chu, The role of hydride, martensite and atomic hydrogen in hydrogen-induced delayed fracture of TiNi alloy, Materials Science and Engineering : A, vol.364, issue.1, p.333338, 2004.

Q. Kan, W. Yan, G. Kang, and Q. Sun, OliverPharr indentation method in determining elastic moduli of shape memory alloysA phase transformable material, Journal of the Mechanics and Physics of Solids, vol.61, issue.10, p.20152033, 2013.

K. Kaneko, K. Yokoyama, K. Moriyama, K. Asaoka, and J. Sakai, Degradation in performance of orthodontic wires caused by hydrogen absorption during short-term immersion in 2.0% acidulated phosphate uoride solution, The Angle Orthodontist, vol.74, issue.4, p.487495, 2004.

D. C. Lagoudas, Shape memory alloys : modeling and engineering applications, 2008.

D. C. Lagoudas and P. B. Entchev, Modeling of transformation-induced plasticity and its eect on the behavior of porous shape memory alloys. part I : constitutive model for fully dense smas, Mechanics of Materials, vol.36, issue.9, p.865892, 2004.

S. Leclercq and C. Lexcellent, A general macroscopic description of the thermomechanical behavior of shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.44, issue.6, p.953959957980, 1996.

J. Lemaitre, J. L. Chaboche, and A. K. Maji, Mechanics of solid materials, Journal of Engineering Mechanics, vol.119, issue.3, p.642643, 1993.

Y. Liang and P. Sofronis, Toward a phenomenological description of hydrogeninduced decohesion at particle matrix interfaces, Journal of the Mechanics and Physics of Solids, vol.51, issue.8, p.15091531, 2003.

Y. Liang, P. Sofronis, and N. Aravas, On the eect of hydrogen on plastic instabilities in metals, Acta Materialia, vol.51, issue.9, p.27172730, 2003.

R. Liu, D. Y. Li, Y. S. Xie, R. Llewellyn, and H. M. Hawthorne, Indentation behavior of pseudoelastic tini alloy, Scripta Materialia, vol.41, issue.7, p.691696, 1999.

J. Lufrano, P. Sofronis, and H. K. Birnbaum, Elastoplastically accommodated hydride formation and embrittlement, Journal of the Mechanics and Physics of Solids, vol.46, issue.9, pp.1497-1520, 1998.

L. G. Machado and M. A. Savi, Medical applications of shape memory alloys, Brazilian Journal of Medical and Biological Research, vol.36, issue.6, p.683691, 2003.

A. Mcnabb and P. K. Foster, A new analysis of the diusion of hydrogen in iron and ferritic steels, Trans. Metall. Soc. AIME, vol.227, issue.3, p.618627, 1963.

T. Merzouki, A. Duval, and T. Ben-zineb, Finite element analysis of a shape memory alloy actuator for a micropump, Simulation Modelling Practice and Theory, vol.27, p.112126, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00730848

D. Mutter and P. Nielaba, Simulation of the shape memory eect in a NiTi nano model system, Journal of Alloys and Compounds, vol.577, pp.83-87, 2013.

S. Nemat-nasser and W. Guo, Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures, Mechanics of materials, vol.38, issue.5, p.463474, 2006.

W. Ni, Y. Cheng, and D. S. Grummon, Microscopic superelastic behavior of a nickeltitanium alloy under complex loading conditions, Applied Physics Letters, vol.82, issue.17, pp.2811-2813, 2003.

R. M. Nieminen, From atomistic simulation towards multiscale modelling of materials, Journal of Physics : Condensed Matter, vol.14, issue.11, p.2859, 2002.

T. Ogawa, K. Yokoyama, K. Asaoka, and J. Sakai, Eects of moisture and dissolved oxygen in methanol and ethanol solutions containing hydrochloric acid on hydrogen absorption and desorption behaviors of NiTi superelastic alloy, Materials Science and Engineering : A, vol.422, issue.1, p.218226, 2006.

L. Onsager, Reciprocal relations in irreversible processes I, Physical review, vol.37, issue.4, p.405, 1931.

L. Onsager, Reciprocal relations in irreversible processes II, Physical review, vol.38, issue.12, p.2265, 1931.

A. Ota, Y. Yazaki, K. Yokoyama, and J. Sakai, Hydrogen absorption and thermal desorption behavior of Ni-Ti superelastic alloy immersed in neutral NaCl and NaF solutions under applied potential, Materials transactions, vol.50, issue.7, p.18431849, 2009.

M. Panico and L. C. Brinson, A three-dimensional phenomenological model for martensite reorientation in shape memory alloys, Journal of the Mechanics and Physics of Solids, vol.55, issue.11, p.24912511, 2007.

E. Patoor and M. Berveiller, Technologie des alliages à mémoire de forme : comportement mécanique et mise en ÷uvre, Hermes, 1994.

E. Patoor, A. Eberhardt, and M. Berveiller, Thermomechanical behavior of shape memory alloys, European Symposium on Martensitic Transformations, p.133140, 1989.

E. Patoor, M. Eberhardt, and . Berveiller, Micromechanical modelling of superelasticity in shape memory alloys, Pitman Research Notes in Mathematics Series, p.3838, 1993.
URL : https://hal.archives-ouvertes.fr/jpa-00254159

E. Patoor, A. Eberhardt, and M. Berveiller, Micromechanical modelling of superelasticity in shape memory alloys, Le Journal de Physique IV, vol.6, issue.C1, p.1277, 1996.
URL : https://hal.archives-ouvertes.fr/jpa-00254159

E. Patoor, M. E. Amrani, A. Eberhardt, and M. Berveiller, Determination of the origin for the dissymmetry observed between tensile and compression tests on shape memory alloys, Le Journal de Physique IV, vol.5, issue.C2, p.2495, 1995.
URL : https://hal.archives-ouvertes.fr/jpa-00253662

A. R. Pelton, C. Trépanier, X. Gong, A. Wick, and K. C. Chen, Structural and diusional eects of hydrogen in TiNi, SMST-2003 : Proceedings of the Fourth International Conference on Shape Memory and Superelastic Technologies, p.3342, 2004.

L. Petrini and F. Migliavacca, Biomedical applications of shape memory alloys, Journal of Metallurgy, vol.2011, p.15, 2011.

B. Peultier, T. B. Zineb, and E. Patoor, Macroscopic constitutive law of shape memory alloy thermomechanical behaviour. application to structure computation by FEM, Mechanics of Materials, vol.38, issue.5, p.510524, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01769307

B. Peultier, T. B. Zineb, and E. Patoor, A simplied micromechanical constitutive law adapted to the design of shape memory applications by nite element methods, Materials Science and Engineering : A, vol.481, p.384388, 2008.

P. Popov and D. C. Lagoudas, A 3d constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of selfaccommodated martensite, International Journal of Plasticity, vol.23, issue.10, p.16791720, 2007.

B. Raniecki and C. Lexcellent, Rlmodels of pseudoelasticity and their specication for some shape memory solids, European journal of mechanics. A. Solids, vol.13, issue.1, p.2150, 1994.

B. Raniecki and C. Lexcellent, Thermodynamics of isotropic pseudoelasticity in shape memory alloys, European Journal of Mechanics-A/Solids, vol.17, issue.2, p.185205, 1998.

O. K. Rediniotis, L. N. Wilson, D. C. Lagoudas, and M. M. Khan, Development of a shapememory-alloy actuated biomimetic hydrofoil, Journal of Intelligent Material Systems and Structures, vol.13, issue.1, p.3549, 2002.

S. W. Robertson, On the mechanical properties and microstructure of Nitinol for biomedical stent applications, 2006.

A. Runciman, K. C. Chen, A. R. Pelton, and C. Trépanier, Eects of hydrogen on the phases and transition temperatures of NiTi, Proceedings of the International Conference on Shape Memory and Superelastic Technologies, p.185, 2006.

J. Ryhänen, Biocompatibility evaluation of nickel-titanium shape memory metal alloy. Oulun yliopisto, 1999.

R. Schmidt, M. Schlereth, H. Wipf, W. Assmus, and M. Mullner, Hydrogen solubility and diusion in the shapememory alloy NiTi, Journal of Physics : Condensed Matter, vol.1, issue.14, p.24732482, 1989.

P. Sofronis and H. K. Birnbaum, Mechanics of the hydrogen dislocation impurity interactionsI. increasing shear modulus, Journal of the Mechanics and Physics of Solids, vol.43, issue.1, p.4990, 1995.

P. Sofronis and R. M. Mcmeeking, Numerical analysis of hydrogen transport near a blunting crack tip, Journal of the Mechanics and Physics of Solids, vol.37, issue.3, p.317350, 1989.

A. Taha and P. Sofronis, A micromechanics approach to the study of hydrogen transport and embrittlement, Engineering Fracture Mechanics, vol.68, issue.6, p.803837, 2001.

K. Takashima, K. Yokoyama, K. Asaoka, and J. Sakai, Eects of potential on hydrogen absorption and desorption behaviors of titanium in neutral uoride solutions, Journal of alloys and compounds, vol.431, issue.1, p.203207, 2007.

K. Tanaka, A phenomenological description on thermomechanical behavior of shape memory alloys, Journal of Pressure Vessel Technology, vol.112, issue.2, p.158163, 1990.

K. Tanaka, S. Kobayashi, and Y. Sato, Thermomechanics of transformation pseudoelasticity and shape memory eect in alloys, International Journal of Plasticity, vol.2, issue.1, p.5972, 1986.

P. Thamburaja, Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys, Journal of the Mechanics and Physics of Solids, vol.53, issue.4, p.825856, 2005.

P. Thamburaja and L. Anand, Polycrystalline shape-memory materials : eect of crystallographic texture, Journal of the Mechanics and Physics of Solids, vol.49, issue.4, p.709737, 2001.

P. Thamburaja and L. Anand, Superelastic behavior in tensiontorsion of an initiallytextured TiNi shape-memory alloy, International Journal of Plasticity, vol.18, issue.11, p.16071617, 2002.

P. Thamburaja and L. Anand, Thermo-mechanically coupled superelastic response of initially-textured TiNi sheet, Acta Materialia, vol.51, issue.2, p.325338, 2003.

P. Thamburaja and N. Nikabdullah, A macroscopic constitutive model for shape-memory alloys : theory and nite-element simulations, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.9, p.10741086, 2009.

P. Thamburaja, H. Pan, and F. S. Chau, Martensitic reorientation and shapememory eect in initially textured polycrystalline TiNi sheet, Acta materialia, vol.53, issue.14, p.38213831, 2005.

P. Thamburaja, H. Pan, and F. S. Chau, The evolution of microstructure during twinning : Constitutive equations, nite-element simulations and experimental verication, International Journal of Plasticity, vol.25, issue.11, p.21412168, 2009.

M. Tomita, K. Yokoyama, K. Asaoka, and J. Sakai, Hydrogen thermal desorption behavior of NiTi superelastic alloy subjected to tensile deformation after hydrogen charging, Materials Science and Engineering : A, vol.476, issue.1, p.308315, 2008.

M. Tomita, K. Yokoyama, and J. Sakai, Eects of potential, temperature and pH on hydrogen absorption and thermal desorption behaviors of NiTi superelastic alloy in 0.9% nacl solution, Corrosion Science, vol.50, issue.7, p.20612069, 2008.

W. Van-moorleghem, M. Chandrasekaran, D. Reynaerts, J. Peirs, and H. Van-brussel, Shape memory and superelastic alloys : the new medical materials with growing demand, Bio-medical materials and engineering, vol.8, issue.2, p.5560, 1998.

G. Venturini, K. Wang, I. Romero, M. P. Ariza, and M. Ortiz, Atomistic long-term simulation of heat and mass transport, Journal of the Mechanics and Physics of Solids, vol.73, p.242268, 2014.

N. Wade, Y. Adachi, and Y. Hosoi, A role of hydrogen in shape memory eect of TiNi alloys, Scripta Metallurgica et Materialia, vol.24, issue.6, p.10511055, 1990.

M. P. Walker, R. J. White, and K. S. Kula, Eect of uoride prophylactic agents on the mechanical properties of nickel-titanium-based orthodontic wires, American journal of orthodontics and dentofacial orthopedics, vol.127, issue.6, p.662669, 2005.

S. K. Yadav, V. Sehgal, and S. Mittal, Eects of uoride on NiTi orthodontic archwires : An x-ray diraction study, Journal of Indian Orthodontic Society, vol.47, 2013.

K. Yokoyama, K. Hamada, K. Moriyama, and K. Asaoka, Degradation and fracture of NiTi superelastic wire in an oral cavity, Biomaterials, vol.22, issue.16, p.22572262, 2001.

K. Yokoyama, A. Nagaoka, and J. Sakai, Eects of the hydrogen absorption conditions on the hydrogen embrittlement behavior of Ni-Ti superelastic alloy, ISIJ International, vol.52, issue.2, p.255262, 2012.

K. Yokoyama, T. Ogawa, K. Asaoka, and J. Sakai, Hydrogen absorption of titanium and nickel-titanium alloys during long-term immersion in neutral uoride solution, Journal of Biomedical Materials Research Part B : Applied Biomaterials, vol.78, issue.1, p.204210, 2006.

K. Yokoyama, T. Ogawa, K. Takashima, K. Asaoka, and J. Sakai, Hydrogen embrittlement of NiTi superelastic alloy aged at room temperature after hydrogen charging, Materials Science and Engineering : A, vol.466, issue.1, p.106113, 2007.

K. Yokoyama, K. Takashima, and J. Sakai, Susceptibility to hydrogen absorption and hydrogen thermal desorption of titanium alloys immersed in neutral uoride solution under applied potential, Materials transactions, vol.49, issue.7, p.16611666, 2008.

K. Yokoyama, M. Tomita, K. Asaoka, and J. Sakai, Hydrogen absorption and thermal desorption behaviors of NiTi superelastic alloy subjected to sustained tensile-straining test with hydrogen charging, Scripta materialia, vol.57, issue.5, p.393396, 2007.

K. Yokoyama, M. Tomita, and J. Sakai, Hydrogen embrittlement behavior induced by dynamic martensite transformation of NiTi superelastic alloy, Acta Materialia, vol.57, issue.6, pp.1875-1885, 2009.

K. Yokoyama, S. Watabe, K. Hamada, J. Sakai, K. Asaoka et al., Susceptibility to delayed fracture of niti superelastic alloy, Materials Science and Engineering : A, vol.341, issue.1, p.9197, 2003.

T. Yoneyama and S. Miyazaki, Shape memory alloys for biomedical applications, 2008.

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, p.24272454, 2007.

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, p.24552490, 2007.

T. Zhang and J. E. Hack, The equilibrium concentration of hydrogen atoms ahead of a mixed mode Imode III crack tip in single crystal iron, Metallurgical and Materials Transactions A, vol.30, issue.1, p.155159, 1999.

Y. Zhong, K. Gall, and T. Zhu, Atomistic characterization of pseudoelasticity and shape memory in NiTi nanopillars, Acta Materialia, vol.60, issue.18, p.63016311, 2012.