American Institute of Mathematical Sciences

T. Aiki and N. Kenmochi, Some models for shape memory alloys,, Mathematical aspects of modelling structure formation phenomena, 17 (2002), 144. Google Scholar

M. Arndt, M. Griebel and T. Roubíček, Modelling and numerical simulation of martensitic transformation in shape memory alloys,, Contin. Mech. Thermodyn., 15 (2003), 463. doi: 10.1007/s00161-003-0127-3. Google Scholar

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). Google Scholar

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. doi: 10.1002/gamm.201110014. Google Scholar

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. doi: 10.1142/S0218202508002632. Google Scholar

F. Auricchio and 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. doi: 10.1002/nme.619. Google Scholar

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. doi: 10.1002/nme.1086. Google Scholar

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. doi: 10.1002/nme.1087. Google Scholar

F. Auricchio, A. Reali and U. Stefanelli, A three-dimensional model describing stress-induces solid phase transformation with permanent inelasticity,, Int. J. Plasticity, 23 (2007), 207. doi: 10.1016/j.ijplas.2006.02.012. Google Scholar

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. doi: 10.1016/j.cma.2009.01.019. Google Scholar

N. Barrera, P. Biscari and M. F. Urbano, Macroscopic modeling of functional fatigue in shape memory alloys,, Eur. J. Mech. A/Solids, (). Google Scholar

S. Bartels and T. Roubíček, Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion,, Math. Modelling Numer. Anal., 45 (2011), 477. doi: 10.1051/m2an/2010063. Google Scholar

B. Benesova, M. Frost and P. Sedlak, A microscopically motivated constitutive model for shape memory alloys: formulation, analysis and computations,, Preprint NCMM/2013/17, (). Google Scholar

A.-L. Bessoud and U. Stefanelli, Magnetic shape memory alloys: Three-dimensional modeling and analysis,, Math. Models Meth. Appl. Sci., 21 (2011), 1043. doi: 10.1142/S0218202511005246. Google Scholar

A.-L. Bessoud, M. Kružík and U. Stefanelli, A macroscopic model for magnetic shape memory alloys,, Preprint IMATI-CNR, (2010). Google Scholar

A. Berti, C. Giorgi and E. Vuk, Free energies and pseudo-elastic transitions for shape memory alloys,, Discrete Cont. Dyn. S. - Series S, 6 (2013), 293. Google Scholar

V. Berti, M. Fabrizio and D. Grandi, Phase transitions in shape memory alloys: A non-isothermal Ginburg-Landau model,, Physica D, 239 (2010), 95. doi: 10.1016/j.physd.2009.10.005. Google Scholar

H. Brézis, Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,, Math Studies, (1973). Google Scholar

M. Brokate and J. Sprekels, Hysteresis and Phase Transitions,, Applied Mathematical Sciences, (1996). doi: 10.1007/978-1-4612-4048-8. Google Scholar

M. Brokate and J. Sprekels, Optimal control of shape memory alloys with solid-solid phase transitions,, in Emerging applications in free boundary problems (Montreal, (1990), 208. Google Scholar

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. doi: 10.1080/01630569808816840. Google Scholar

P. Colli and J. Sprekels, Global existence for a three-dimensional model for the thermodynamical evolution of shape memory alloys,, Nonlinear Anal., 18 (1992), 873. doi: 10.1016/0362-546X(92)90228-7. Google Scholar

T. W. Duerig and A. R. Pelton editors, SMST-2003 Proceedings of the International Conference on Shape Memory and Superelastic Technology Conference,, ASM International, (2003). Google Scholar

M. Eleuteri, J. Kopfová and P. Krejčí, A thermodynamic model for material fatigue under cyclic loading,, Physica B: Condensed Matter, 407 (2012), 1415. doi: 10.1016/j.physb.2011.10.017. Google Scholar

M. Eleuteri, J. Kopfová and P. Krejčí, Non-isothermal cyclic fatigue in an oscillating elastoplastic beam,, Comm. Pure Appl. Anal., 12 (2013), 2973. doi: 10.3934/cpaa.2013.12.2973. Google Scholar

M. Eleuteri, J. Kopfová and P. Krejčí, Fatigue accumulation in a thermo-visco-elastoplastic plate,, Discrete Cont. Dyn. S. Series B, 19 (2014). Google Scholar

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. doi: 10.3934/nhm.2011.6.145. Google Scholar

M. Eleuteri, L. Lussardi and U. Stefanelli, Thermal control of the Souza-Auricchio model for shape memory alloys,, Discrete Cont. Dyn. S. - Series S, 6 (2013), 369. Google Scholar

V. Evangelista, S. Marfia and E. Sacco, Phenomenological 3D and 1D consistent models for shape-memory alloy materials,, Comput. Mech., 44 (2009), 405. doi: 10.1007/s00466-009-0381-8. Google Scholar

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. Google Scholar

F. Falk, Martensitic domain boundaries in shape-memory alloys as solitary waves,, J. Phys. C4 Suppl., 12 (1982), 3. Google Scholar

F. Falk and P. Konopka, Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys,, J. Phys. Condens. Matter, 2 (1990), 61. doi: 10.1088/0953-8984/2/1/005. Google Scholar

M. Frémond, Matériaux à mémoire de forme,, C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, 304 (1987), 239. Google Scholar

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. doi: 10.1007/s00161-011-0221-x. Google Scholar

K.-H. Hoffmann, M. Niezgódka and S. Zheng, Existence and uniqueness to an extended model of the dynamical developments in shape memory alloys,, Nonlinear Anal., 15 (1990), 977. doi: 10.1016/0362-546X(90)90079-V. Google Scholar

K.-H. Hoffmann and D. Tiba, Control of a plate with nonlinear shape memory alloy reinforcements,, Adv. Math. Sci. Appl., 7 (1997), 427. Google Scholar

K.-H. Hoffmann and A. Z. Ochowski, Control of the thermoelastic model of a plate activated by shape memory alloy reinforcements,, Math. Methods Appl. Sci., 21 (1998), 589. doi: 10.1002/(SICI)1099-1476(19980510)21:7<589::AID-MMA904>3.0.CO;2-D. Google Scholar

O. Klein, Stability and uniqueness results for a numerical appproximation of the thermomechanical phase transitions in shape memory alloys,, Adv. in Math. Sci. and Appl., 5 (1995), 91. Google Scholar

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. doi: 10.1051/m2an/2010024. Google Scholar

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. doi: 10.1177/1081286510386935. Google Scholar

G. A. Maugin, The Thermomechanics of Plasticity and Fracture,, Cambridge Texts in Applied Mathematics. Cambridge University Press, (1992). doi: 10.1017/CBO9781139172400. Google Scholar

A. Mielke, Evolution of rate-independent systems,, in Handbook of Differential Equations, 2 (2005), 461. Google Scholar

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. doi: 10.1137/080726215. Google Scholar

A. Mielke, L. Paoli, A. Petrov and U. Stefanelli, Error estimates for discretizations of a rate-independent variational inequality,, SIAM J. Numer. Anal., 48 (2010), 1625. doi: 10.1137/090750238. Google Scholar

A. Mielke and A. Petrov, Thermally driven phase transformation in shape-memory alloys,, Adv. Math. Sci. Appl., 17 (2007), 667. Google Scholar

A. Mielke and F. Theil, On rate-independent hysteresis models,, NoDEA, 11 (2004), 151. doi: 10.1007/s00030-003-1052-7. Google Scholar

L. Paoli and A. Petrov, Global existence result for phase transformations with heat transfer in shape memory alloys,, Preprint WIAS, (2011). Google Scholar

I. Pawłow, Three-dimensional model of thermomechanical evolution of shape memory materials,, Control Cybernet., 29 (2000), 341. Google Scholar

F. Rindler, Optimal control for nonconvex rate-independent evolution processes,, SIAM J. Control Optim., 47 (2008), 2773. doi: 10.1137/080718711. Google Scholar

F. Rindler, Approximation of rate-independent optimal control problems,, SIAM J. Numer. Anal., 47 (2009), 3884. doi: 10.1137/080744050. Google Scholar

R. Rossi and M. Thomas, From an adhesive to a brittle delamination model in thermo-visco-elasticity,, Quaderno 05/2012 del Seminario Matematico di Brescia, (2012), 1. Google Scholar

T. Roubíček, Thermodynamics of rate independent processes in viscous solids at small strains,, SIAM J. Math. Anal., 42 (2010), 256. doi: 10.1137/080729992. Google Scholar

T. Roubíček and G. Tomassetti, Thermodynamics of shape-memory alloys under electric current,, Zeit. angew. Math. Phys., 61 (2010), 1. doi: 10.1007/s00033-009-0007-1. Google Scholar

T. Roubíček and G. Tomassetti, Phase transformations in electrically conductive ferromagnetic shape-memory alloys, their thermodynamics and analysis,, Arch. Rat. Mech. Anal., (). doi: 10.1007/s00205-013-0648-2. Google Scholar

A. Sadjadpour and K. Bhattacharya, A micromechanics-inspired constitutive model for shape-memory alloys,, Smart Mater. Struct., 16 (2007), 1751. doi: 10.1088/0964-1726/16/5/030. Google Scholar

J. Sokołowski and J. Sprekels, Control problems with state constraints for shape memory alloys,, Math. Methods Appl. Sci., 17 (1994), 943. doi: 10.1002/mma.1670171204. Google Scholar

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. doi: 10.1016/S0997-7538(98)80005-3. Google Scholar

U. Stefanelli, Magnetic control of magnetic shape-memory single crystals,, Phys. B, 407 (2012), 1316. doi: 10.1016/j.physb.2011.06.043. Google Scholar

G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part I: Existence and discretization in time,, SIAM Journal on Control and Optimization (SICON), 50 (2012), 2836. doi: 10.1137/110839187. Google Scholar

G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part II: regularization and differentiability,, Preprint SPP1253-119, (2011), 1253. Google Scholar

G. Wachsmuth, Optimal control of quasistatic plasticity with linear kinematic hardening, Part III: optimality conditions,, Preprint SPP1253-119, (2011), 1253. Google Scholar

S. Yoshikawa, I. Pawłow and W. M. Zajączkowski, Quasi-linear thermoelasticity system arising in shape memory materials,, SIAM J. Math. Anal., 38 (2007), 1733. doi: 10.1137/060653159. Google Scholar