`a`
Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

The Souza-Auricchio model for shape-memory alloys
Pages: 723 - 747, Issue 4, August 2015

doi:10.3934/dcdss.2015.8.723      Abstract        References        Full text (584.8K)           Related Articles

Diego Grandi - Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria (email)
Ulisse Stefanelli - Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria (email)

1 T. Aiki, A model of 3D shape memory alloy materials, J. Math. Soc. Japan, 57 (2005), 903-933.       
2 M. Arndt, M. Griebel and T. Roubíček, Modelling and numerical simulation of martensitic transformation in shape memory alloys, Contin. Mech. Thermodyn., 15 (2003), 463-485.       
3 M. Arrigoni, F. Auricchio, V. Cacciafesta, L. Petrini and R. Pietrabissa, Cyclic effects in shape-memory alloys: A one-dimensional continuum model, J. Phys. IV France, 11 (2001), 577-582.
4 E. Artioli, F. Auricchio and R. L. Taylor, A beam finite element for nonlinear analysis of shape memory alloy devices, in New Trends in Thin Structures: Formulation, Optimization and Coupled Problems (eds. P. Wriggers and P. de Mattos Pimenta), CISM International Centre for Mechanical Sciences, 519, Springer-Verlag, New-York, 2010, 59-97.
5 E. Artioli, S. Marfia, E. Sacco and R. L. Taylor, A nonlinear plate finite element formulation for shape memory alloy applications, Internat. J. Numer. Meth. Engrg., 89 (2012), 1249-1271.       
6 F. Auricchio, A.-L. Bessoud, A. Reali and U. Stefanelli, Macroscopic modeling of magnetic shape memory alloys, Oberwolfach Reports, 14 (2010), 771-773.
7 F. Auricchio, A.-L. Bessoud, A. Reali and U. Stefanelli, A three-dimensional phenomenological models for magnetic shape memory alloys, GAMM-Mitt., 34 (2011), 90-96.       
8 F. Auricchio, A.-L. Bessoud, A. Reali and U. Stefanelli, A phenomenological model for the magneto-mechanical response of single-crystal magnetic shape memory alloys, preprint IMATI-CNR, 3PV13/3/0, 2013.
9 F. Auricchio, E. Boatti, A. Reali and U. Stefanelli, The GENERIC formulation of coupled thermomechanical response in shape-memory alloys, in preparation, 2013.
10 F. Auricchio and E. Bonetti, A new "flexible'' 3D macroscopic model for shape memory alloys, Discrete Contin. Dyn. Syst. Ser. S, 6 (2013), 277-291.       
11 F. Auricchio and J. Lubliner, A uniaxial model for shape-memory alloys, Internat. J. Solids Structures, 34 (1997), 3601-3618.
12 F. Auricchio, A. Mielke and U. Stefanelli, A rate-independent model for the isothermal quasi-static evolution of shape-memory materials, Math. Models Meth. Appl. Sci., 18 (2008), 125-164.       
13 F. Auricchio, L. Petrini, Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations, Internat. J. Numer. Methods Engrg., 55 (2002), 1255-1284.       
14 F. Auricchio and L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations. Part I: Solution algorithm and boundary value problems, Internat. J. Numer. Meth. Engrg., 61 (2004), 807-836.       
15 F. Auricchio and L. Petrini, A three-dimensional model describing stress-temperature induced solid phase transformations. Part II: Thermomechanical coupling and hybrid composite applications, Internat. J. Numer. Meth. Engrg., 61 (2004), 716-737.
16 F. Auricchio, A. Reali and U. Stefanelli, A three-dimensional model describing stress-induces solid phase transformation with residual plasticity, Int. J. Plasticity, 23 (2007), 207-226.
17 F. Auricchio, A. Reali and U. Stefanelli, A phenomenological 3D model describing stress-induced solid phase transformations with permanent inelasticity, in Topics on Mathematics for Smart Systems (eds. B. Miara, G. Stavroulakis and V. Valente), World Sci. Publ., Hackensack, NJ, 2007, 1-14.       
18 F. Auricchio, A. Reali and U. Stefanelli, A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties, Comput. Methods Appl. Mech. Engrg., 198 (2009), 1631-1637.       
19 F. Auricchio and U. Stefanelli, Well-posedness and approximation for a one-dimensional model for shape memory alloys, Math. Models Meth. Appl. Sci., 15 (2005), 1301-1327.       
20 K. Bhattacharya, Microstructures of Martensites, Oxford Series on Materials Modeling, Oxford University Press, Oxford, 2003.       
21 V. Berti, M. Fabrizio and D. Grandi, Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau model, Phys. D, 239 (2010), 95-102.
22 V. Berti, M. Fabrizio and D. Grandi, Hysteresis and phase transitions for one-dimensional and three-dimensional models in shape memory alloys, J. Math. Phys., 51 (2010), 062901, 13 pp.       
23 A.-L. Bessoud and U. Stefanelli, Magnetic shape memory alloys: Three-dimensional modeling and analysis, Math. Models Meth. Appl. Sci., 21 (2011), 1043-1069.       
24 A.-L. Bessoud, M. Kružík and U. Stefanelli, A macroscopic model for magnetic shape memory alloys, Z. Angew. Math. Phys., 64 (2013), 343-359.       
25 H. Brézis, Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, Math. Studies, Vol.5, North-Holland, Amsterdam/New York, 1973.       
26 Z. Bo and D. Lagoudas, Thermomechanical modeling of polycrystalline SMAs under cyclic loading. Part III: Evolution of plastic strains and two- way shape memory effect, Int. J. Engrg. Sci., 37 (1999), 1175-1203.       
27 E. Bonetti, Global solvability of a dissipative Frémond model for shape memory alloys. I. Mathematical formulation and uniqueness, Quart. Appl. Math., 61 (2003), 759-781.       
28 M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Applied Mathematical Sciences, 121, Springer-Verlag, New York, 1996.       
29 W. F. Brown, Jr., Magnetoelastic Interactions, Springer, Berlin, 1966.
30 N. Bubner, J. Sokołowski and J. Sprekels, Optimal boundary control problems for shape memory alloys under state constraints for stress and temperature, Numer. Funct. Anal. Optim., 19 (1998), 489-498.       
31 P. Colli, Global existence for the three-dimensional Frémond model of shape memory alloys, Nonlinear Anal., 24 (1995), 1565-1579.       
32 P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys, Quart. Appl. Math., 48 (1990), 31-47.       
33 S. Conti, M. Lenz and M. Rumpf, Macroscopic behaviour of magnetic shape-memory polycrystals and polymer composites, Mater. Sci. Engrg. A, 481-482 (2008), 351-355.
34 B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, Second ed., Wiley., 2008.
35 F. Daghia, M. Fabrizio and D. Grandi, A non isothermal Ginzburg-Landau model for phase transitions in shape memory alloys, Meccanica, 45 (2010), 797-807.       
36 R. Delville, B. Malard, J. Pilch, P. Šittner and D. Schryvers, Microstructure changes during non-conventional heat treatment of thin Ni-Ti wires by pulsed electric current studied by transmission electron microscopy, Acta Mater., 58 (2010), 4503-4515.
37 R. Delville, B. Malard, J. Pilch, P. Šittner and D. Schryvers, Transmission electron microscopy study of microstructural evolution in nanograined Ni-Ti microwires heat treated by electric pulse, Solid State Phenom., 172-174 (2011), 682-687.
38 A. DeSimone and R. D. James, A constrained theory of magnetoelasticity, J. Mech. Phys. Solids, 50 (2002), 283-320.       
39 T. W. Duerig and A. R. Pelton, eds., SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference, ASM International, 2003.
40 J. Dutkiewicz, Plastic deformation of CuAlMn shape-memory alloys, J. Mat. Sci., 29 (1994), 6249-6254.
41 M. Eleuteri, L. Lussardi and U. Stefanelli, A rate-independent model for permanent inelastic effects in shape memory materials, Netw. Heterog. Media, 6 (2011), 145-165.       
42 M. Eleuteri and L. Lussardi, Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials, Evol. Equ. Control Theory, 3 (2014), 411-427.
43 M. Eleuteri, L. Lussardi and U. Stefanelli, Thermal control of the Souza-Auricchio model for shape memory alloys, Discrete Cont. Dyn. Syst.-S, 6 (2013), 369-386.       
44 V. Evangelista, S. Marfia and E. Sacco, Phenomenological 3D and 1D consistent models for shape-memory alloy materials, Comput. Mech., {44} (2009), 405-421.       
45 V. Evangelista, S. Marfia and E. Sacco, A 3D SMA constitutive model in the framework of finite strain, Internat. J. Numer. Methods Engrg., 81 (2010), 761-785.
46 F. Falk, Model free energy, mechanics and thermodynamics of shape memory alloys, Acta Metal., 28 (1980), 1773-1780.
47 F. Falk and P. Konopka, Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys, Continuum Models of Discrete Systems, 123-125 (1990), 113-122.
48 G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. Reine Angew. Math., 595 (2006), 55-91.       
49 M. Frémond, Matériaux à mémoire de forme, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, 304 (1987), 239-244.
50 M. Frémond, Non-Smooth Thermomechanics, Springer-Verlag, Berlin, 2002.       
51 M. Frémond and S. Miyazaki, Shape Memory Alloys, CISM Courses and Lectures, Vol. 351, Springer-Verlag, 1996.
52 M. Frémond and E. Rocca, A model for shape memory alloys with the possibility of voids, Discrete Contin. Dyn. Syst., 27 (2010), 1633-1659.       
53 S. Frigeri, P. Krejčí and U. Stefanelli, Quasistatic isothermal evolution of shape memory alloys, Math. Models Meth. Appl. Sci., 21 (2011), 2409-2432.       
54 S. Frigeri and U. Stefanelli, Existence and time-discretization for the finite-strain Souza-Auricchio constitutive model for shape-memory alloys, Contin. Mech. Thermodyn., 24 (2012), 63-77.       
55 J.-Y. Gauthier, C. Lexcellent, A. Hubert, J. Abadie and N. Chaillet, Magneto-thermo-mechanical modeling of a magnetic shape memory alloy Ni-Mn-Ga single crystal, Ann. Solid Struct. Mech., 2 (2001), 19-31.
56 S. Govindjee and C. Miehe, A multi-variant martensitic phase transformation model: Formulation and numerical implementation, Comput. Methods Appl. Mech. Engrg., 191 (2001), 215-238.
57 S. Govindjee and E. P. Kasper, A shape memory alloy model for uranium- niobium accounting for plasticity, J. Intelligent Mat. Syst. Struct., 8 (1997), 815-823.
58 D. Grandi and U. Stefanelli, Modeling microstructure-dependent inelasticity in shape-memory alloys, preprint, IMATI-CNR 13PV13/11/0, 2013.
59 D. Helm and P. Haupt, Shape memory behaviour: Modelling within continuum thermomechanics, Intern. J. Solids Struct., 40 (2003), 827-849.
60 L. Hirsinger and C. Lexcellent, Internal variable model for magneto-mechanical behaviour of ferromagnetic shape memory alloys Ni-Mn-Ga, J. Phys. IV, 112 (2003), 977-980.
61 K.-H. Hoffmann, M. Niezgódka and Z. Songmu, Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys, Nonlinear Anal., 15 (1990), 977-990.       
62 K.-H. Hoffmann and D. Tiba, Control of a plate with nonlinear shape memory alloy reinforcements, Adv. Math. Sci. Appl., 7 (1997), 427-436.       
63 K.-H. Hoffmann and A. Żochowski, Control of the thermoelastic model of a plate activated by shape memory alloy reinforcements, Math. Methods Appl. Sci., 21 (1998), 589-603.       
64 R. D. James and M. Wuttig, Magnetostriction of martensite, Phil. Mag. A, 77 (1998), 1273-1299.
65 H. E. Karaca, I. Karaman, B. Basaran, Y. I. Chumlyakov and H. J. Maier, Magnetic field and stress induced martensite reorientation in NiMnGa ferromagnetic shape memory alloy single crystals, Acta Mat., 54 (2006), 233-245.
66 J. Kiang and L. Tong, Modelling of magneto-mechanical behaviour of Ni-Mn-Ga single crystals, J. Magn. Magn. Mater., 292 (2005), 394-412.
67 B. Kiefer, A Phenomelogical Model for Magnetic Shape Memory Alloys, Ph.D Thesis, Texas A&M, 2006.
68 B. Kiefer and D. C. Lagoudas, Modeling the coupled strain and magnetization response of magnetic shape memory alloys under magnetomechanical loading, J. Intell. Mater. Syst. Struct., 20 (2009), 143-170.
69 B. Kiefer, H. Karaca, D. C. Lagoudas and I. Karaman, Characterization and modeling of the magnetic field-induced strain and work output in Ni$_2$MnGa magnetic shape memory alloys, J. Magn. Magn. Mater., 312 (2007), 164-175.
70 P. Krejčí and U. Stefanelli, Existence and nonexistence for the full thermomechanical Souza-Auricchio model of shape memory wires, Math. Mech. Solids, 16 (2011), 349-365.       
71 P. Krejčí and U. Stefanelli, Well-posedness of a thermo-mechanical model for shape memory alloys under tension, M2AN Math. Model. Numer. Anal., 44 (2010), 1239-1253.       
72 M. Kružík and J. Zimmer, A model of shape memory alloys taking into account plasticity, IMA J. Appl. Math., 76 (2011), 193-216.       
73 D. C. Lagoudas and P. Entchev, Modeling of transformation-induced plas- ticity and its effect on the behavior of porous shape memory alloys. Part I: Constitutive model for fully dense SMAs, Mech. Mat., 36 (2004), 865-892.
74 D. C. Lagoudas, P. B. Entchev, P. Popov, E. Patoor, L. C. Brinson and X. Gao, Shape memory alloys, Part II: Modeling of polycrystals, Mech. Materials, 38 (2006), 430-462.
75 E. Lee, Elastic-plastic deformation at finite strains, J. Appl. Mech, 36 (1969), 1-6.
76 V. I. Levitas, Thermomechanical theory of martensitic phase transformations in inelastic materials, Intern. J. Solids Struct., 35 (1998), 889-940.       
77 Ch. Lexcellent, Shape-Memory Alloys Handbook, Wiley, 2013.
78 A. A. Likhachev and K. Ullakko, Magnetic-field-controlled twin boundaries motion and giant magneto-mechanical effects in Ni-Mn-Ga shape memory alloy, Phys. Lett. A, 275 (2000), 142-151.
79 B. Malard, J. Pilch, P. Šittner, R. Delville and C. Curfs, In situ investigation of the fast microstructure evolution during electropulse treatment of cold drawn NiTi wires, Acta Mater., 59 (2011), 1542-1556.
80 A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. Partial Differential Equations, 22 (2005), 73-99.       
81 M. Maraldi, L. Molari and D. Grandi, A non-isothermal phase-field model for shape memory alloys: Numerical simulations of superelasticity and shape memory effect under stress- controlled conditions, J. Intelligent Mat. Syst. Struct., 23 (2012), 1083-1092.
82 M. Maraldi, L. Molari and D. Grandi, A macroscale, phase-field model for shape memory alloys with non-isothermal effects: Influence of strain-rate and environmental conditions on the mechanical response, Acta Mat., 60 (2012), 179-191.
83 C. Miehe, B. Kiefer and D. Rosato, An incremental variational formulation of dissipative magnetostriction at the macroscopic continuum level, Internat. J. Solids Struct., 48 (2011), 1846-1866.
84 A. Mielke, Evolution of rate-independent systems, in Handbook of Differential Equations, Evolutionary Equations (eds. C. Dafermos and E. Feireisl), Elsevier, II, 2005, 461-559.       
85 A. Mielke, Formulation of thermoelastic dissipative material behavior using GENERIC, Contin. Mech. Thermodyn., 23 (2011), 233-256.       
86 A. Mielke, On thermodynamically consistent models and gradient structures for thermoplasticity, GAMM Mitt., 34 (2011), 51-58.       
87 A. Mielke, L. Paoli and A. Petrov, On existence and approximation for a 3D model of thermally induced phase transformations in shape-memory alloys, SIAM J. Math. Anal., 41 (2009), 1388-1414.       
88 A. Mielke, L. Paoli, A. Petrov, U. Stefanelli, Error estimates for space-time discretizations of a rate-independent variational inequality, SIAM J. Numer. Anal., 48 (2010), 1625-1646.       
89 A. Mielke, L. Paoli, A. Petrov and U. Stefanelli, Error bounds for space-time discretizations of a 3d model for shape-memory materials, in IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials (ed. K. Hackl), IUTAM Bookseries, 21, Springer, 2010, 185-197.
90 A. Mielke and A. Petrov, Thermally driven phase transformation in shape-memory alloys, Adv. Math. Sci. Appl., 17 (2007), 667-685.       
91 A. Mielke and F. Rindler, Reverse approximation of energetic solutions to rate-independent processes, NoDEA Nonlinear Differential Equations Appl., 16 (2009), 17-40.       
92 A. Mielke, T. Roubíček and U. Stefanelli, $\Gamma$-limits and relaxations for rate-independent evolutionary problems, Calc. Var. Partial Differential Equations, 31 (2008), 387-416.       
93 A. Mielke and U. Stefanelli, Linearized plasticity is the evolutionary $\Gamma$-limit of finite plasticity, J. Eur. Math. Soc. (JEMS), 15 (2013), 923-948.       
94 A. Mielke and F. Theil, On rate-independent hysteresis models, NoDEA Nonlinear Diff. Equations Applications, 11 (2004), 151-189.       
95 S. J. Murray, M. Marioni, P. G. Tello, S. M. Allen and R. C. O'Handley, Giant magnetic-field-induced strain in Ni-Mn-Ga crystals: Experimental results and modeling, J. Magn. Magn. Mater., 226-230 (2001), 945-947.
96 S. J. Murray, S. M. Allen, R. C. O'Handley and T. A. Lograsso, Magnetomechanical performance and mechanical properties of Ni-Mn-Ga ferromagnetic shape memory alloys, in SPIE Proceedings 3992, Smart Structures and Materials 2000: Active Materials: Behavior and Mechanics, 2000, 387.
97 S. J. Murray, R. C. O'Handley and S. M. Allen, Model for discontinuous actuation of ferromagnetic shape memory alloy under stress, J. Appl. Phys., 89 (2000), 1295-1301.
98 R. C. O'Handley, Model for strain and magnetization in magnetic shape-memory alloys, J. Appl. Phys., 83 (1998), 3263-3270.
99 R. C. O'Handley, S. J. Murray, M. Marioni, H. Nembach and S. M. Allen, Phenomenology of giant magnetic-field-induced strain in ferromagnetic shape-memory materials, J. Appl. Phys., 87 (200), 4712-4717.
100 A. Paiva, M. A. Savi, A. M. B. Braga and P. M. C. L. Pacheco, A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity, Int. J. Solids Struct., 42 (2005), 3439-3457.
101 I. Pawłow and W. M. Zajaczkowski, Global existence to a three-dimensional non-linear thermoelasticity system arising in shape memory materials, Math. Methods Appl. Sci., 28 (2005), 407-442.       
102 L. Paoli and A. Petrov, Global existence result for phase transformations with heat transfer in shape memory alloys, preprint, arXiv:1104.5408, 2011.
103 L. Paoli and A. Petrov, Existence result for a class of generalized standard materials with thermomechanical coupling, preprint, arXiv:1111.2436, 2011.
104 L. Paoli and A. Petrov, Thermodynamics of multiphase problems in viscoelasticity, GAMM-Mitt., 35 (2012), 75-90.       
105 L. Paoli and A. Petrov, Global existence result for thermoviscoelastic problems with hysteresis, Nonlinear Anal. Real World Appl., 13 (2012), 524-542.       
106 L. Paoli and A. Petrov, Solvability for a class of generalized standard materials with thermomechanical coupling, Nonlinear Anal. Real World Appl., 14 (2013), 111-130.       
107 I. Pawłow and A. Żochowski, A Control Problem for a Thermoelastic System in Shape Memory Materials. Free Boundary Problems, (Japanese), Sūrikaisekikenkyūsho Kōkyūroku, No. 1210, (2001), 8-23.       
108 B. Peultier, T. Ben Zineb and E. Patoor, Macroscopic constitutive law for SMA: Application to structure analysis by FEM, Materials Sci. Engrg. A, 438-440 (2006), 454-458.
109 P. Popov and D. C. Lagoudas, A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite, Int. J. Plasticity, 23 (2007), 1679-1720.
110 B. Raniecki and Ch. Lexcellent, $R_L$ models of pseudoelasticity and their specification for some shape-memory solids, Eur. J. Mech. A Solids, 13 (1994), 21-50.       
111 S. Reese and D. Christ, Finite deformation pseudo-elasticity of shape memory alloys - Constitutive modelling and finite element implementation, Int. J. Plasticity, 24 (2008), 455-482.
112 F. Rindler, Optimal control for nonconvex rate-independent evolution processes, SIAM J. Control Optim., 47 (2008), 2773-2794.       
113 F. Rindler, Approximation of rate-independent optimal control problems, SIAM J. Numer. Anal., 47 (2009), 3884-3909.       
114 T.Roubíček, Models of microstructure evolution in shape memory alloys, in Nonlinear Homogenization and its Appl.to Composites, Polycrystals and Smart Materials, (eds. P. Ponte Castaneda, J. J. Telega, B. Gambin), NATO Sci. Series II, 170, Kluwer, Dordrecht, 2004, 269-304.       
115 T. Roubíček, Rate-independent processes in viscous solids at small strains, Math. Methods Appl. Sci., 32 (2009), 825-862.       
116 T. Roubíček, Thermodynamics of rate-independent processes in viscous solids at small strains, SIAM J. Math. Anal., 42 (2010), 256-297.       
117 T. Roubíček, Approximation in multiscale modelling of microstructure evolution in shape-memory alloys, Cont. Mech. Thermodynam., 23 (2011), 491-507.       
118 T. Roubíček, Nonlinearly coupled thermo-visco-elasticity, NoDEA Nonlinear Differential Equations Appl., 20 (2013), 1243-1275.       
119 T. Roubíček and U. Stefanelli, Magnetic shape-memory alloys: Thermomechanical modeling and analysis, preprint, IMATI-CNR 6PV13/0/0, 2013.
120 T. Roubíček and G. Tomassetti, Thermodynamics of shape-memory alloys under electric current, Z. Angew. Math. Phys., 61 (2010), 1-20.       
121 T. Roubíček and G. Tomassetti, Phase transformations in electrically conductive ferromagnetic shape-memory alloys, their thermodynamics and analysis, Arch. Ration. Mech. Anal., 210 (2013), 1-43.       
122 P. Šittner, Y. Hara and M. Tokuda, Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces, Metall. Materials Trans., 26 (1995), 2923-2935.
123 J. Sokołowski and J. Sprekels, Control problems with state constraints for shape memory alloys, Math. Methods Appl. Sci., 17 (1994), 943-952.       
124 A. C. Souza, E. N. Mamiya and N. Zouain, Three-dimensional model for solids undergoing stress-induced tranformations, Eur. J. Mech. A Solids, 17 (1998), 789-806.
125 A. Sozinov, A. A. Likhachev, N. Lanska and K. Ullakko, Giant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase, Appl. Phys. Lett., 80 (2002), 1746-1748.
126 U. Stefanelli, Analysis of a thermomechanical model for shape memory alloys, SIAM J. Math. Anal., 37 (2005), 130-155.       
127 U. Stefanelli, Magnetic control of magnetic shape-memory single crystals, Phys. B, 407 (2012), 1316-1321.
128 P. Thamburaja and L. Anand, Polycrystalline shape-memory materials: Effect of crystallographic texture, J. Mech. Phys. Solids, 49 (2001), 709-737.
129 R. Tickle and R. D. James, Magnetic and magnetomechanical properties of $Ni_2MnGa$, J. Magn. Magn. Mater., 195 (1999), 627-638.
130 R. A. Vandermeer, J. C. Ogle and W. G. Jr. Northcutt, A phenomenological study of the shape memory effect in polycrystalline Uranium-Niobium alloys, Metal. Trans A, 12A (1981), 733-741.
131 A. Visintin, Differential Models of Hysteresis, Applied Mathematical Sciences, 111, Springer, Berlin, 1994.       
132 G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part I: Existence and discretization in time, SIAM J. Control Optim., 50 (2012), 2836-2861.       
133 G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, part II: Regularization and differentiability, preprint, SPP1253-119, 2011.
134 G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, part III: Optimality conditions, preprint, SPP1253-119, 2011.
135 J. Wang and P. Steinmann, A variational approach towards the modelling of magnetic field-induced strains in magnetic shape memory alloys, J. Mech. Phys. Solids, 60 (2012), 1179-1200.       
136 S. Yoshikawa, I. Pawłow and W. M. Zajaczkowski, Quasi-linear thermoelasticity system arising in shape memory materials, SIAM J. Math. Anal., 38 (2007), 1733-1759.       
137 J. Zimmer, Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy, J. Math. Anal. Appl., 292 (2004), 589-604.       

Go to top