F. Auricchio, E. Bonetti, G. Scalet, and F. Ubertini, Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation, International Journal of Plasticity, vol.59, pp.30-54, 2014.
DOI : 10.1016/j.ijplas.2014.03.008

F. Auricchio, M. Conti, M. Ferraro, S. Morganti, A. Reali et al., Innovative and efficient stent flexibility simulations based on isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.295, pp.347-361, 2015.
DOI : 10.1016/j.cma.2015.07.011

F. Auricchio, S. Morganti, and A. Reali, SMA numerical modeling versus experimental results, ESOMAT 2009, 8th European Symposium on Martensitic Transformations, pp.1-6, 2009.
DOI : 10.1051/esomat/200908004

F. Auricchio and L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems, International Journal for Numerical Methods in Engineering, vol.61, issue.6, pp.807-836, 2004.
DOI : 10.1002/nme.1086

F. Auricchio, A. Reali, and U. Stefanelli, A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity, International Journal of Plasticity, vol.23, issue.2, pp.207-226, 2007.
DOI : 10.1016/j.ijplas.2006.02.012

F. Auricchio, A. Reali, and U. Stefanelli, A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.17-20, pp.1631-1637, 2009.
DOI : 10.1016/j.cma.2009.01.019

F. Auricchio, G. Scalet, and M. Urbano, A Numerical/Experimental Study of Nitinol Actuator Springs, Journal of Materials Engineering and Performance, vol.6, issue.676, pp.2420-2428, 2014.
DOI : 10.1007/s11665-014-0883-1

N. Barrera, P. Biscari, and M. Urbano, Macroscopic modeling of functional fatigue in shape memory alloys, European Journal of Mechanics - A/Solids, vol.45, pp.101-109, 2014.
DOI : 10.1016/j.euromechsol.2013.11.015

T. Bartel and K. Hackl, A micromechanical model for martensitic phase-transformations in shape-memory alloys based on energy-relaxation, ZAMM, vol.455, issue.482, p.792809, 2009.
DOI : 10.1002/zamm.200900244

T. Bartel and K. Hackl, Multiscale modeling of martensitic phase transformations: on the numerical determination of heterogeneous mesostructures within shape-memory alloys induced by precipitates, p.324342, 2010.

T. Bartel, A. Menzel, and B. Svendsen, Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity, Journal of the Mechanics and Physics of Solids, vol.59, issue.5, pp.1004-1019, 2011.
DOI : 10.1016/j.jmps.2011.02.006

E. Boatti, M. Ferraro, G. Scalet, and F. Auricchio, Development of an effective and user-friendly numerical framework for the simulation of complex smart material components and devices, Abstract of the First International Conference on Materials Design and Applications, 2016.

H. Brézis, Opérateurs maximum monotones et semigroupes de contractions dans les espaces de Hilbert, 1972.

C. Carstensen, K. Hackl, and A. Mielke, Non-convex potentials and microstructures in finite-strain plasticity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.458, issue.2018, pp.299-317, 2002.
DOI : 10.1098/rspa.2001.0864

Y. Chemisky, G. Chatzigeorgiou, P. Kumar, and D. Lagoudas, A constitutive model for cyclic actuation of high-temperature shape memory alloys, Mechanics of Materials, vol.68, pp.120-136, 2014.
DOI : 10.1016/j.mechmat.2013.07.020

URL : https://hal.archives-ouvertes.fr/hal-01199736

C. Cisse, W. Zaki, and T. B. Zineb, A review of constitutive models and modeling techniques for shape memory alloys, International Journal of Plasticity, vol.76, pp.244-284, 2016.
DOI : 10.1016/j.ijplas.2015.08.006

URL : https://hal.archives-ouvertes.fr/hal-01415862

B. D. Coleman and W. Noll, The termodynamics of elastic mmaterial with heat conduction and viscosity, Arch. Ration. Mech. Anal, issue.13, pp.167-178, 1963.

R. Dhote, H. Gomez, R. Melnik, and J. Zu, 3D coupled thermo-mechanical phase-field modeling of shape memory alloy dynamics via isogeometric analysis, Computers & Structures, vol.154, pp.48-58, 2015.
DOI : 10.1016/j.compstruc.2015.02.017

V. Evangelista, S. Marfia, and E. Sacco, Phenomenological 3D and 1D consistent models for shape-memory alloy materials, Computational Mechanics, vol.17, issue.3, pp.405-421, 2009.
DOI : 10.1007/s00466-009-0381-8

D. Grandi and U. Stefanelli, A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys, Meccanica, vol.544, issue.9, pp.2265-2283, 2014.
DOI : 10.1007/s11012-014-0018-7

D. Grandi and U. Stefanelli, The Souza-Auricchio model for shape-memory alloys, Discrete and Continuous Dynamical Systems -Series S, pp.723-747, 2015.
DOI : 10.3934/dcdss.2015.8.723

M. Gurtin, An Introduction to Continuum Mechanics, Journal of Applied Mechanics, vol.51, issue.4, 1981.
DOI : 10.1115/1.3167763

D. Hartl, Y. Chemisky, and F. Meraghni, Three-dimensional constitutive model considering transformation-induced damage and resulting fatigue failure in shape memory alloys, Proc SPIE 9058, p.905805, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01199560

D. Hartl and D. Lagoudas, Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys, Smart Materials and Structures, vol.18, issue.10, 2009.
DOI : 10.1088/0964-1726/18/10/104017

R. Jähne, Multiaxial mechanical characterization and constitutive modeling of superelastic sheets for solid-state hinges, 2012.

J. Jani, M. Leary, A. Subic, and M. Gibson, A review of shape memory alloy research, applications and opportunities, Materials & Design (1980-2015), vol.56, pp.1078-1113, 2014.
DOI : 10.1016/j.matdes.2013.11.084

B. Kiefer, T. Bartel, and A. Menzel, Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response, Smart Materials and Structures, vol.21, issue.9, pp.1-8, 2012.
DOI : 10.1088/0964-1726/21/9/094007

J. Korelc, Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes, Engineering with Computers, vol.18, issue.4, pp.312-327, 2002.
DOI : 10.1007/s003660200028

D. Lagoudas, Shape Memory Alloys: Modeling and Engineering Applications, 2008.

D. C. Lagoudas, D. J. Hartl, Y. Chemisky, L. Machado, and P. Popov, Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys, International Journal of Plasticity, vol.32, issue.33, pp.32-33, 2012.
DOI : 10.1016/j.ijplas.2011.10.009

C. Lexcellent, S. Leclercq, B. Gabry, and G. Bourbon, The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological model, International Journal of Plasticity, vol.16, issue.10-11, pp.1155-1168, 2000.
DOI : 10.1016/S0749-6419(00)00005-X

URL : https://hal.archives-ouvertes.fr/hal-00591125

N. Meisel, A. Elliott, and C. Williams, A procedure for creating actuated joints via embedding shape memory alloys in PolyJet 3D printing, Journal of Intelligent Material Systems and Structures, vol.133, issue.12, pp.1498-1512, 2015.
DOI : 10.1177/1045389X14544144

C. Miehe, J. Schotte, and M. Lambrecht, Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals, Journal of the Mechanics and Physics of Solids, vol.50, issue.10, pp.2123-2167, 2002.
DOI : 10.1016/S0022-5096(02)00016-9

M. Ortiz and E. Repetto, Nonconvex energy minimization and dislocation structures in ductile single crystals, Journal of the Mechanics and Physics of Solids, vol.47, issue.2, pp.397-462, 1999.
DOI : 10.1016/S0022-5096(97)00096-3

H. Pan, P. Thamburaja, and F. Chau, Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning, International Journal of Plasticity, vol.23, issue.4, pp.711-732, 2007.
DOI : 10.1016/j.ijplas.2006.08.002

M. Peigney and J. Seguin, An incremental variational approach to coupled thermo-mechanical problems in anelastic solids. Application to shape-memory alloys, International Journal of Solids and Structures, vol.50, issue.24, pp.4043-4054, 2013.
DOI : 10.1016/j.ijsolstr.2013.08.013

URL : https://hal.archives-ouvertes.fr/hal-01111474

M. Peigney, J. Seguin, and E. Hervé-luanco, Numerical simulation of shape memory alloys structures using interior-point methods, International Journal of Solids and Structures, vol.48, issue.20, pp.2791-2799, 2011.
DOI : 10.1016/j.ijsolstr.2011.05.017

URL : https://hal.archives-ouvertes.fr/hal-00875256

E. Peraza-hernandez, D. Hartl, E. Galvan, and R. Malak, Design and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet, Journal of Mechanical Design, vol.135, issue.11, pp.1-11, 2013.
DOI : 10.1115/1.4025382

P. Popov and D. Lagoudas, A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite, International Journal of Plasticity, vol.23, issue.10-11, pp.1679-1720, 2007.
DOI : 10.1016/j.ijplas.2007.03.011

M. A. Qidwai and D. Lagoudas, Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms, International Journal for Numerical Methods in Engineering, vol.9, issue.18, pp.1123-1168, 2000.
DOI : 10.1002/(SICI)1097-0207(20000228)47:6<1123::AID-NME817>3.0.CO;2-N

A. Quarteroni, Numerical Models for Differential Problems, 2009.
DOI : 10.1007/978-88-470-1071-0

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

G. Scalet, F. Auricchio, and D. Hartl, Efficiency and effectiveness of implicit and explicit approaches for the analysis of shape-memory alloy bodies, Journal of Intelligent Material Systems and Structures, vol.49, issue.6, 2015.
DOI : 10.1177/1045389X14560366

P. Sedlák, M. Frost, B. Benesová, T. B. Zineb, and P. Sittner, Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings, International Journal of Plasticity, vol.39, pp.132-151, 2012.
DOI : 10.1016/j.ijplas.2012.06.008

A. Souza, E. Mamiya, and N. Zouain, Three-dimensional model for solids undergoing stress-induced phase transformations, European Journal of Mechanics - A/Solids, vol.17, issue.5, pp.789-806, 1998.
DOI : 10.1016/S0997-7538(98)80005-3

A. Stebner and L. Brinson, Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys, Computer Methods in Applied Mechanics and Engineering, vol.257, pp.17-35, 2013.
DOI : 10.1016/j.cma.2012.12.021

S. Stupkiewicz and H. Petryk, A robust model of pseudoelasticity in shape memory alloys, International Journal for Numerical Methods in Engineering, vol.85, issue.15, pp.747-769, 2013.
DOI : 10.1002/nme.4405

K. Tanaka and S. Nagaki, Eine thermomechanische Beschreibung von Materialien mit inneren Variablen beim Phasen???bergang, Ingenieur-Archiv, vol.15, issue.5, pp.287-299, 1982.
DOI : 10.1007/BF00536655

C. M. Wayman, Engineering Aspects of Shape Memory Alloys)1, Ch. An introduction to martensite and shape memory, Butterworth-Heinemann, pp.3-20, 1989.

M. Wilkins, Calculation of elastic-plastic flow, In: Methods of Computational Physics, vol.3, 1964.

W. Zaki, Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers, International Journal of Solids and Structures, vol.49, issue.21, pp.2951-2961, 2012.
DOI : 10.1016/j.ijsolstr.2012.05.038

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