Aiki T.: A model of 3D shape memory alloy materials. J. Math. Soc. Jpn. 57, 903–933 (2005)
Arndt M., Griebel M., Roubıv cek T.: Modelling and numerical simulation of martensitic transformation in shape memory alloys. Contin. Mech. Thermodyn. 15, 463–485 (2003)
Auricchio, F., Bessoud, A.-L., Reali, A., Stefanelli, U.: A phenomenological model for the magneto-mechanical response of Magnetic Shape Memory Alloys single crystals. Preprint IMATI-CNR 3PV13/3/0 (2013)
Auricchio F., Bessoud A.-L., Reali A., Stefanelli U.: A three-dimensional phenomenological models for magnetic shape memory alloys. GAMM-Mitt. 34, 90–96 (2011)
Auricchio F., Bonetti E.: A new ‘flexible’ 3D macroscopic model for shape memory alloys. Discret. Contin. Dyn. Syst. Ser. S 6, 277–291 (2013)
Auricchio F., Lubliner J.: A uniaxial model for shape-memory alloys. Int. J. Solids Struct. 34, 3601–3618 (1997)
Auricchio F., Mielke A., Stefanelli U.: A rate-independent model for the isothermal quasi-static evolution of shape-memory materials. Math. Models Meth. Appl. Sci. 18, 125–164 (2008)
Auricchio F., Petrini L.: Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations. Int. J. Numer. Methods Eng. 55, 1255–1284 (2002)
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. Meth. Eng. 61, 807–836 (2004)
Auricchio F., Petrini L.: A three-dimensional model describing stress-temperature induced solid phase transformations. Part II: Thermomechanical coupling and hybrid composite applications. Int. J. Numer. Meth. Eng. 61, 716–737 (2004)
Auricchio, F., Reali, A., Stefanelli, U.: A phenomenological 3D model describing stress-induced solid phase transformations with permanent inelasticity. In: Topics on Mathematics for Smart Systems, pp. 1–14. World Sci. Publ., Hackensack, NJ (2007)
Auricchio F., Reali A., Stefanelli U.: A three-dimensional model describing stress-induces solid phase transformation with residual plasticity. Int. J. Plast. 23, 207–226 (2007)
Auricchio F., Reali A., Stefanelli U.: A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties. Comput. Methods Appl. Mech. Eng. 198, 1631–1637 (2009)
Berti, V., Fabrizio, M.,Grandi, D.: Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys. J. Math. Phys. 51 062901, 13 pp. (2010)
Bessoud A.-L., Kruží k M., Stefanelli U.: A macroscopic model for magnetic shape-memory single crystals. Z. Angew. Math. Phys. 64, 343–359 (2013)
Bessoud A.-L., Stefanelli U.: Magnetic shape memory alloys: three-dimensional modeling and analysis. Math. Models Meth. Appl. Sci. 21, 1043–1069 (2011)
Boccardo L., Gallouët T.: Non-linear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87, 149–169 (1989)
Bonetti E.: Global solvability of a dissipative Frémond model for shape memory alloys. I. Mathematical formulation and uniqueness. Q. Appl. Math. 61, 759–781 (2003)
Bonetti E., Colli P., Laurencot P.: Global existence for a hydrogen storage model with full energy balance. Nonlinear Anal.: Th. Meth. Appl. 75, 3558–3573 (2012)
Brézis H.: Équations et inéquations non-linéaires dans les espaces vectoriel en dualité. Ann. Inst. Fourier 18, 115–176 (1968)
Brézis H.: Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les espaces de Hilbert, Math Studies, Vol. 5 North-Holland. North-Holland, Amsterdam/New York (1973)
BrokateM. Sprekels J.: Hysteresis and Phase Transitions. Springer, New York (1996)
Colli P.: Global existence for the three-dimensional Frémond model of shape memory alloys. Nonlinear Anal. 24, 1565–1579 (1995)
Colli P., Frémond M., Visintin A.: Thermo-mechanical evolution of shape memory alloys. Q. Appl. Math. 48, 31–47 (1990)
Conti S., Lenz M., Rumpf M.: Macroscopic behaviour of magnetic shape-memory polycrystals and polymer composites. Mater. Sci. Eng. A 481–482(7), 351–355 (2008)
Cullity B.D., Graham C.D.: Introduction to Magnetic Materials. 2nd edn. Wiley, New York (2008)
Daghia F., Fabrizio M., Grandi D.: A non isothermal GinzburgZ–Landau model for phase transitions in shape memory alloys. Meccanica 45, 797–807 (2010)
Delville R., Malard B., Pilch J., Šittner P., Schryvers D.: Microstructure changes during non-conventional heat treatment of thin Ni–Ti wires by pulsed electric current studied by transmission electron microscopy. Acta Mater. 58, 4503–4515 (2010)
DeSimone A., James R.D.: A constrained theory of magnetoelasticity. J. Mech. Phys. Solids 50, 283–320 (2002)
Duerig, T.W., Pelton, A.R. (eds.): SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference. ASM International (2003)
Duvaut G., Lions J.-L.: Inequalities in Mechanics and Physics. Springer, Berlin (1976)
Eleuteri M., Lussardi L., Stefanelli U.: A rate-independent model for permanent inelastic effects in shape memory materials. Netw. Heterog. Medi 6, 145–165 (2011)
Eleuteri M., Lussardi L., Stefanelli U.: Thermal control of the Souza-Auricchio model for shape memory alloys. Discret. Contin. Dyn. Syst.-S 6, 369–386 (2013)
Evangelista V., Marfia S., Sacco E.: Phenomenological 3D and 1D consistent models for shape-memory alloy materials. Comput. Mech. 44, 405–421 (2009)
Evangelista V., Marfia S., Sacco E.: A 3D SMA constitutive model in the framework of finite strain. Int. J. Numer. Methods Eng. 81, 761–785 (2010)
Falk F.: Model free energy, mechanics and thermodynamics of shape memory alloys. Acta Metallurgica 28, 1773–1780 (1980)
Falk F., Konopka P.: Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys. J. Phys.: Condens. Matter 2, 61 (1990)
Frémond M.: Matériaux à à mémoire de forme. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre 304, 239–244 (1987)
Frémond M.: Non-Smooth Thermomechanics. Springer, Berlin (2002)
Frémond M., Miyazaki S.: Shape Memory Alloys. CISM Courses and Lectures, vol. 351. Springer, Berlin (1996)
Frigeri S., Stefanelli U.: Existence and time-discretization for the finite-strain Souza-Auricchio constitutive model for shape-memory alloys. Contin. Mech. Thermodyn. 24, 63–77 (2012)
Giusti E.: Direct Methods in the Calculus of Variations. World Scientific, New Yersey (2003)
Grandi, D., Stefanelli, U.:A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys. Preprint IMATI-CNR 13PV13/11/0 (2013)
Govindjee S., Miehe C.: A multi-variant martensitic phase transformation model: formulation and numerical implementation. Comput. Methods Appl. Mech. Eng. 191, 215–238 (2001)
Helm D., Haupt P.: Shape memory behaviour: modelling within continuum thermomechanics. Int. J. Solids Struct. 40, 827–849 (2003)
Hirsinger L., Lexcellent C.: Internal variable model for magneto-mechanical behaviour of ferromagnetic shape memory alloys Ni–Mn–Ga. J. Phys. IV 112, 977–980 (2003)
Hoffmann K.-H., Niezgódka M., Songmu Z.: Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys. Nonlinear Anal. 15, 977–990 (1990)
James R.D., Wuttig M.: Magnetostriction of martensite. Phil. Mag. A 77, 1273–1299 (1998)
Karaca H.E., Karaman I., Basaran B., Chumlyakov Y.I., Maier H.J.: Magnetic field and stress induced martensite reorientation in NiMnGa ferromagnetic shape memory alloy single crystals. Acta Mat. 54, 233–245 (2006)
Kiang J., Tong L.: Modelling of magneto-mechanical behaviour of Ni–Mn–Ga single crytals. J. Magn. Magn. Mater. 292, 394–412 (2005)
Kiefer, B.: A Phenomelogical Model for Magnetic Shape Memory Alloys. PhD Thesis, Texas A&M University (2006)
Kiefer B., Lagoudas D.C.: Modeling the coupled strain and magnetization response of magnetic shape memory alloys under magnetomechanical loading. J. Intell. Mater. Syst. Struct. 20, 143–170 (2009)
Krejčí P., Stefanelli U.: Existence and nonexistence for the full thermomechanical Souza-Auricchio model of shape memory wires. Math. Mech. Solids 16, 349–365 (2011)
Krejčí P., Stefanelli U.: Well-posedness of a thermo-mechanical model for shape memory alloys under tension. M2AN Math. Model. Numer. Anal. 44, 1253–1253 (2010)
Kruží k M., Zimmer J.: A model of shape memory alloys taking into account plasticity. IMA J. Appl. Math. 76, 193–216 (2011)
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)
Levitas V.I.: Thermomechanical theory of martensitic phase transformations in inelastic materials. Int. J. Solids Struct. 35, 889–940 (1998)
Likhachev A.A., Ullakko K.: Magnetic-field-controlled twin boundaries motion and giant magneto-mechanical effects in Ni2MnGa shape memory alloy. Phys. Lett. A 275, 142–151 (2000)
Miehe C., Rosato D., Kiefer B.: Variational principles in dissipative electro-magneto-mechanics: a framework for the macro-modeling of functional materials. Int. J. Numer. Methods Eng. 86, 1225–1276 (2011)
Miehe, C., Kiefer, B., Rosato, D.: An incremental variational formulation of dissipative magnetostriction at the macroscopic continuum level. Int. J. Solids Struct. 48, 1846–1866 (2011)
Mielke A., Paoli L., Petrov A.: On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys. SIAM J. Math. Anal. 41, 1388–1414 (2009)
Mielke A., Paoli L., Petrov A., Stefanelli U.: Error estimates for space-time discretizations of a rate-independent variational inequality. SIAM J. Numer. Anal. 48, 1625–1646 (2010)
Mielke, A., Paoli, L., Petrov, A., Stefanelli, U.: Error bounds for space-time discretizations of a 3D model for shape-memory materials. In: Hackl, K. (ed.) IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, pp. 185–197. Springer, Berlin (2010)
Mielke A., Petrov A.: Thermally driven phase transformation in shape-memory alloys. Adv. Math. Sci. Appl. 17, 667–685 (2007)
Mielke A., Roubíček T., Stefanelli U.: Γ-imits and relaxations for rate-independent evolutionary problems. Calc. Var. Partial Differ. Equ. 31, 387–416 (2008)
O’Handley R.C.: Model for strain and magnetization in magnetic shape-memory alloys. J. Appl. Phys. 83, 3263–3270 (1998)
Paoli, L., Petrov, A.: Global Existence Result for Phase Transformations with Heat Transfer in Shape Memory Alloys. WIAS Preprint n. 1608 (2011)
Paoli L., Petrov A.: Global existence result for thermoviscoelastic problems with hysteresis. Nonlinear Anal. Real World Appl. 13, 524–542 (2012)
Paoli L., Petrov A.: Thermodynamics of multiphase problems in viscoelasticity. GAMM-Mitt. 35, 75–90 (2012)
Paoli, L., Petrov, A.: Existence Result for a Class of Generalized Standard Materials with Thermomechanical Coupling. WIAS Preprint n. 1635 (2011)
Paoli L., Petrov A.: Solvability for a class of generalized standard materials with thermomechanical coupling. Nonlinear Anal. Real World Appl. 14, 111–130 (2013)
Pawłow I., Zajaczkowski W.M.: Global existence to a three-dimensional non-linear thermoelasticity system arising in shape memory materials. Math. Methods Appl. Sci. 28, 407–442 (2005)
Peultier B., Ben Zineb T., Patoor E.: Macroscopic constitutive law for SMA: application to structure analysis by FEM. Mater. Sci. Eng. A 438(440), 454–458 (2006)
Podio-Guidugli P., Roubíček T., Tomassetti G.: A thermodynamically-consistent theory of the ferro/paramagnetic transition. Arch. Ration. Mech. Anal. 198, 1057–1094 (2010)
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)
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)
Reese S., Christ D.: Finite deformation pseudo-elasticity of shape memory alloys—constitutive modelling and finite element implementation. Int. J. Plast. 24, 455–482 (2008)
Roubíček, T.: Models of microstructure evolution in shape memory materials. In: Ponte, P., Castaneda, et al. (eds.) Nonlin. Homogen. and its Appl. to Composites, Polycryst. and Smart Mater. NATO Sci. Ser. II/170, pp. 269–304. Kluwer, Dordrecht (2004)
Roubíček T.: Approximation in multiscale modelling of microstructure evolution in shape-memory alloys. Cont. Mech. Thermodyn. 23, 491–507 (2011)
Roubíček T.: Nonlinear Partial Differential Equations with Applications. 2nd edn. Birkhäuser, Basel (2013)
Roubíček T., Tomassetti G.: Thermodynamics of shape-memory alloys under electric current. Zeit. Angew. Math. Phys. 61, 1–20 (2010)
Roubíček T., Tomassetti G.: Ferromagnets with eddy currents and pinning effects: their thermodynamics and analysis. Math. Models Methods Appl. Sci. 21, 29–55 (2011)
Roubíček T., Tomassetti G.: Phase transformations in electrically conductive ferromagnetic shape-memory alloys, their thermodynamics and analysis. Arch. Ration. Mech. Anal. 210, 1–43 (2013)
Souza A.C., Mamiya E.N., Zouain N.: Three-dimensional model for solids undergoing stress-induced tranformations. Eur. J. Mech. A Solids 17, 789–806 (1998)
Sadjadpour A., Bhattacharya K.: A micromechanics-inspired constitutive model for shape-memory alloys. Smart Mater. Struct. 16, 1751–1765 (2007)
Sedlák P., Frost M., Benešová B., Ben Zineb T., Šittner P.: Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings. Int. J. Plast. 39, 132–151 (2012)
Stefanelli U.: Analysis of a thermomechanical model for shape memory alloys. SIAM J. Math. Anal. 37, 130–155 (2005)
Stefanelli U.: Magnetic control of magnetic shape-memory crystals. Physics B 407, 1316–1321 (2012)
Thamburaja P., Anand L.: Polycrystalline shape-memory materials: effect of crystallographic texture. J. Mech. Phys. Solids 49, 709–737 (2001)
Tickle R., James R.D.: Magnetic and magnetomechanical properties of Ni 2 MnGa. J. Magn. Magn. Mater. 195, 627–638 (1999)
Wang J., Steinmann P.: A variational approach towards the modeling of magnetic field-induced strains in magnetic shape memory alloys. J. Mech. Phys. Solids 60, 1179–1200 (2012)
Yoshikawa, S., Pawłow, I., Zajaczkowski, W.M.: Quasi-linear thermoelasticity system arising in shape memory materials. SIAM J. Math. Anal. 38, 1733–1759 (2007); (electronic)
Zimmer J.: Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy. J. Math. Anal. Appl. 292, 589–604 (2004)