[1]
|
R. Alessi and D. Bernardini, Analysis of localization phenomena in shape memory alloys bars by a variational approach, Int. J. Solids Struct., 73/74 (2015), 113-133.
doi: 10.1016/j.ijsolstr.2015.06.021.
|
[2]
|
J. Arghavani, F. Auricchio, R. Naghdabadi, A. Reali and S. Sohrabpour, A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings, Int. J. Plast., 26 (2010), 976-991.
|
[3]
|
K. M. Armattoe, C. Bouby, M. Haboussi and T. B. Zineb, Modeling of latent heat effects on phase transformation in shape memory alloy thin structures, Int. J. Solids Struct., 88/89 (2016), 283-295.
doi: 10.1016/j.ijsolstr.2016.02.024.
|
[4]
|
K. Armattoe, M. Haboussi and T. B. Zineb, A 2D finite element based on a nonlocal constitutive model describing localization and propagation of phase transformation in shape memory alloy thin structures, Int. J. Solids Struct., 51 (2014), 1208-1220.
doi: 10.1016/j.ijsolstr.2013.11.028.
|
[5]
|
F. Auricchio, D. Fugazza and R. Desroches, Rate-dependent thermo-mechanical modelling of superelastic shape-memory alloys for seismic applications, Journal of Intelligent Material Systems and Structures, 19 (2008), 47-61.
doi: 10.1177/1045389X06073426.
|
[6]
|
A. Baêta-Neves, M. Savi and P. Pacheco, On the Fremond's constitutive model for shape memory alloys, Mech. Res. Commun., 31 (2004), 677-688.
|
[7]
|
Z. Bažant and M. Jirásek, Nonlocal integral formulations of plasticity and damage: Survey of progress, J. Eng. Mech., 128 (2002), 1119-1149.
|
[8]
|
N. J. Bechle and S. Kyriakides, Localization in NiTi tubes under bending, Int. J. Sol, 51 (2014), 967-980.
doi: 10.1016/j.ijsolstr.2013.11.023.
|
[9]
|
B. Benešová and T. Roubíček, Micro-to-meso scale limit for shape-memory-alloy models with thermal coupling, Multiscale Model. Simul, 10 (2012), 1059-1089.
doi: 10.1137/110852176.
|
[10]
|
K. Bhattacharya, P. Purohit and B. Craciun, Mobility of twin and phase boundaries, J. de Physique IV, 112 (2003), 163-166.
doi: 10.1051/jp4:2003856.
|
[11]
|
L. Boccardo and T. Gallouët, Non-linear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0.
|
[12]
|
E. Bonetti, M. Frémond and C. Lexcellent, Global existence and uniqueness for a thermomechanical model for shape memory alloys with partition of the strain, Math. Mech. Solids, 11 (2006), 251-275.
doi: 10.1177/1081286506040403.
|
[13]
|
C. Bouvet, S. Calloch and C. Lexcellent, A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loading, Eur. J. Mech. A, 23 (2004), 37-61.
doi: 10.1016/j.euromechsol.2003.09.005.
|
[14]
|
B.-C. Chang, J. A. Shaw and M. A. Iadicola, Thermodynamics of shape memory alloy wire: Modeling, experiments and application, Continuum Mech. Thermodyn., 18 (2006), 83-118.
doi: 10.1007/s00161-006-0022-9.
|
[15]
|
D. Chatziathanasiou, Y. Chemisky, G. Chatzigeorgiou and F. Meragni, Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading, Int. J. Plast., 82 (2016), 192-224.
doi: 10.1016/j.ijplas.2016.03.005.
|
[16]
|
Y. Chemisky, A. Duval, E. Patoor and T. Ben Zineb, Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation, Mech. Mater., 43 (2011), 361-376.
doi: 10.1016/j.mechmat.2011.04.003.
|
[17]
|
C. Cisse, W. Zaki and T. Ben Zineb, A review of constitutive models and modeling techniques for shape memory alloys, Int. J. Plasticity, 76 (2016), 244-284.
doi: 10.1016/j.ijplas.2015.08.006.
|
[18]
|
C. Cisse, W. Zaki and T. Ben Zineb, A review of modeling techniques for advanced effects in shape memory alloy behavior, Smart Mater. Struct., 25 (2016), 103001.
doi: 10.1088/0964-1726/25/10/103001.
|
[19]
|
T. J. Cognata, D. J. Hartl, R. Sheth and C. Dinsmore, A morphing radiator for high-turndown thermal control of crewed space exploration vehicles, in Proc. 23rd AIAA/AHS Adaptive Structures Conf., (2015), 5–9.
doi: 10.2514/6.2015-1509.
|
[20]
|
P. Colli, Global existence for the three-dimensional Frémond model of shape memory alloys, Nonlinear Analysis, Th. Meth. Appl., 24 (1995), 1565-1579.
doi: 10.1016/0362-546X(94)00097-2.
|
[21]
|
P. Colli, M. Frémond and A. Visintin, Thermo-mechanical evolution of shape memory alloys, Quarterly Appl. Math., 48 (1990), 31-47.
doi: 10.1090/qam/1040232.
|
[22]
|
P. Colli and J. Sprekels, Global existence for a three-dimensional model for the thermo-mechanical evolution of shape memory alloys, Nonlinear Anal., 18 (1992), 873-888.
doi: 10.1016/0362-546X(92)90228-7.
|
[23]
|
P. Colli and A. Visintin, On a class of doubly nonlinear evolution equations, Comm. Part. Diff. Eq., 15 (1990), 737-756.
doi: 10.1080/03605309908820706.
|
[24]
|
F. D. Fischer, J. Svoboda and H. Petryk, Thermodynamic extremal principles for irreversible processes in materials science, Acta Mater., 67 (2014), 1-20.
doi: 10.1016/j.actamat.2013.11.050.
|
[25]
|
M. Frémond, Matériaux à mémoire de forme, C.R. Acad. Sci. Paris Sér.II, 304 (1987), 239-244.
|
[26]
|
M. Frémond and S. Miyazaki, Shape Memory Alloys, Springer, Wien, 1996.
|
[27]
|
M. Frost, B. Benešová and P. Sedlák, A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations, Math. Mech. Solids, 21 (2016), 358-382.
|
[28]
|
M. Frost, B. Benešová, H. Seiner, M. Kružík, P. Šittner and P. Sedlák, Thermomechanical model for NiTi-based shape memory alloys covering macroscopic localization of martensitic transformation, Int. J. Solids Struct., (2020).
doi: 10.1016/j.ijsolstr.2020.08.012.
|
[29]
|
M. Frost, P. Sedlák, L. Kadeřávek, L. Heller and P. Šittner, Modeling of mechanical response of NiTi shape memory alloy subjected to combined thermal and non-proportional mechanical loading: A case study on helical spring actuator, J. Intel. Mat. Syst. Str., 27 (2016), 1927-1938.
|
[30]
|
M. Frost, P. Sedlák, A. Kruisová and M. Landa, Simulations of self-expanding braided stent using macroscopic model of NiTi shape memory alloys covering R-phase, J. Mater. Eng. Perform., 23 (2014), 2584-2590.
doi: 10.1007/s11665-014-0966-z.
|
[31]
|
C. Grabe and O. T. Bruhns, On the viscous and strain rate dependent behavior of polycrystalline NiTi, Int. J. Solids Struct., 45 (2008), 1876-1895.
doi: 10.1016/j.ijsolstr.2007.10.029.
|
[32]
|
X. Gu, W. Zaki, C. Morin, Z. Moumni and W. Zhang, Time integration and assessment of a model for shape memory alloys considering multiaxial nonproportional loading cases, Int. J. Solids Struct., 54 (2015), 28-99.
doi: 10.1016/j.ijsolstr.2014.11.005.
|
[33]
|
M. R. Hajidehi and S. Stupkiewicz, Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys, Int. J. Solids Struct., 135 (2018), 208-218.
|
[34]
|
B. Halphen and Q. S. Nguyen, Sur les matériaux standard généralisés, J. Mécanique, 14 (1975), 39-63.
|
[35]
|
M. A. Iadicola and J. A. Shaw, Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy, Int. J. Plast., 20 (2004), 577-605.
doi: 10.1016/S0749-6419(03)00040-8.
|
[36]
|
K. Jacobus, H. Sehitoglu and M. Balzer, Effect of stress state on the stress-induced martensitic transformation in polycrystalline Ni-Ti alloy, Metall, 27 (1996), 3066-3073.
doi: 10.1007/BF02663855.
|
[37]
|
J. M. Jani, M. Leary, A. Subic and M. A. Gibson, A review of shape memory alloy research, applications and opportunities, Materials and Design, 56 (2014), 1078-1113.
|
[38]
|
D. Jiang, S. Kyriakides and C. M. Landis, Propagation of phase transformation fronts in pseudoelastic niti tubes under uniaxial tension, Extrem Mech. Letters, 15 (2017), 113-121.
doi: 10.1016/j.eml.2017.06.006.
|
[39]
|
M. Jirásek and S. Rolshoven, Localization properties of strain-softening gradient plasticity models, Part Ⅱ: Theories with gradients of internal variables, Int. J. Solids Struct., 46 (2009), 2239-2254.
|
[40]
|
P. Junker and K. Hackl, About the influence of heat conductivity on the mechanical behavior of poly-crystalline shape memory alloys, Int. J. Structural Changes in Solids, 3 (2011), 49-62.
|
[41]
|
P. Junker, J. Makowski and K. Hackl, The principle of the minimum of the dissipation potential for non-isothermal processes, Continuum Mech. Thermodyn., 26 (2014), 259-268.
doi: 10.1007/s00161-013-0299-4.
|
[42]
|
A. Kelly, A. P. Stebner and K. Bhattacharya, A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation, J. Mech. Phys. Solids, 97 (2016), 197-224.
doi: 10.1016/j.jmps.2016.02.007.
|
[43]
|
M. Kružík and T. Roubíček, Mathematical Methods in Continuum Mechanics of Solids, Springer, Cham/Switzerland, 2019.
|
[44]
|
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. Mater., 38 (2006), 430-462.
doi: 10.1016/j.mechmat.2005.08.003.
|
[45]
|
D. C. Lagoudas, D. J. Hartl, Y. Chemisky, L. G. Machado and P. Popov, Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys, Int. J. Plast., 32/33 (2012), 155-183.
doi: 10.1016/j.ijplas.2011.10.009.
|
[46]
|
P. Luig and O. T. Bruhns, On the modeling of shape memory alloys using tensorial internal variables, Mater. Sci. Engr. A, 481/482 (2008), 379-383.
doi: 10.1016/j.msea.2007.03.123.
|
[47]
|
G. A. Maugin, The Thermomechanics of Plasticity and Fracture, Cambridge Univ. Press, 1992.
doi: 10.1017/CBO9781139172400.
|
[48]
|
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.
doi: 10.1137/080726215.
|
[49]
|
A. Mielke and A. Petrov, Thermally driven phase transformation in shape-memory alloys, Adv. Math. Sci. Appl., 17 (2007), 667-685.
|
[50]
|
A. Mielke and T. Roubíček, Rate-Independent Systems: Theory and Application, Springer New York, 2015.
doi: 10.1007/978-1-4939-2706-7.
|
[51]
|
Q. S. Nguyen, Stability and Nonlinear Solid Mechanics, J.Wiley, Chichester, 2000.
|
[52]
|
K. Otsuka and C. M. Wayman, Shape Memory Materials, Cambridge Univ. Press, 1998.
|
[53]
|
H. Petryk, Incremental energy minimization in dissipative solids, R. C. Mécanique, 331 (2003), 469-474.
doi: 10.1016/S1631-0721(03)00109-8.
|
[54]
|
E. A. Pieczyska, H. Tobushi and K. Kulasinski, Development of transformation bands in TiNi SMA for various stress and strain rates studied by a fast and sensitive infrared camera, Smart Mater. Struct., 22 (2013), 035007.
doi: 10.1088/0964-1726/22/3/035007.
|
[55]
|
M. Razaee-Hajidehi, K. Tůma and S. Stupkiewicz, Gradient-enhanced thermomechanical 3D model for simulation of transformation patterns in pseudoelastic shape memory alloys, Int. J. Plasticity, 128 (2020), 102589.
doi: 10.1016/j.ijplas.2019.08.014.
|
[56]
|
B. Reedlunn, C. B. Churchill, E. E. Nelson, J. A. Shaw and S. H. Daly, Tension, compression, and bending of superelastic shape memory alloy tubes, J. Mech. Phys. Solids, 63 (2014), 506-537.
doi: 10.1016/j.jmps.2012.12.012.
|
[57]
|
T. Roubíček, Models of microstructure evolution in shape memory materials, Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, Springer, Dordrecht, 170 (2004), 269–304.
doi: 10.1007/1-4020-2623-4_12.
|
[58]
|
T. Roubíček, Nonlinear Partial Differential Equations with Applications, Birkhäuser, Basel, 2nd edition, 2013.
|
[59]
|
A. Sadjadpour and K. Bhattacharya, A micromechanics-inspired constitutive model for shape-memory alloys, Smart Mater. Struct., 16 (2007), 1751-1765.
doi: 10.1088/0964-1726/16/5/030.
|
[60]
|
A. Sadjadpour and K. Bhattacharya, A micromechanics-inspired constitutive model for shape-memory alloys: The one-dimensional case, Smart Mater. Struct., 16 (2007), S51–S62.
doi: 10.1088/0964-1726/16/1/S06.
|
[61]
|
L. Saint-Sulpice, S. Arbab Chirani and S. Calloch, A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings, Mech. Mater., 41 (2009), 12-26.
doi: 10.1016/j.mechmat.2008.07.004.
|
[62]
|
P. Sedlák, M. Frost, B. Benešová, P. Šittner and T. Ben Zineb, Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings, Int. J. Plast., 39 (2012), 132-151.
|
[63]
|
P. Sedmák, J. Pilch, L. Heller, J. Kopeček, J. Wright, P. Sedlák, M. Frost and P. Šittner, Grain-resolved analysis of localized deformation in nickel-titanium wire under tensile load, Science, 353 (2016), 559-562.
|
[64]
|
J. A. Shaw and S. Kyriakides, On the nucleation and propagation of phase transformation fronts in a NiTi alloy, Acta Mater., 45 (1997), 683-700.
doi: 10.1016/S1359-6454(96)00189-9.
|
[65]
|
P. Šittner, Y. Liu and V. Novák, On the origin of Lüders-like deformation of NiTi shape memory alloys, J. Mech. Phys. Solids, 53 (2005), 1719-1746.
|
[66]
|
A. P. Stebner and L. C. Brinson, Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys, Comput. Methods Appl. Mech. Eng., 257 (2013), 17-35.
doi: 10.1016/j.cma.2012.12.021.
|
[67]
|
S. Stupkiewicz and H. Petryk, A robust model of pseudoelasticity in shape memory alloys, Int. J. Numer. Meth. Engng., 93 (2013), 747-769.
doi: 10.1002/nme.4405.
|
[68]
|
M. Thomasová, H. Seiner, P. Sedlák, M. Frost, M. Ševčík, I. Szurman, R. Kocich, J. Drahokoupil, P. Šittner and M. Landa, Evolution of macroscopic elastic moduli of martensitic polycrystalline NiTi and NiTiCu shape memory alloys with pseudoplastic straining, Acta Materialia, 123 (2017), 146-156.
|
[69]
|
H. Tobushi, Y. Shimeno, T. Hachisuka and K. Tanaka, Influence of strain rate on superelastic properties of TiNi shape memory alloy, Mech. Mater., 30 (1998), 141-150.
doi: 10.1016/S0167-6636(98)00041-6.
|
[70]
|
J. Uchil, K. P. Mohanchandra, K. Ganesh Kumara, K. K. Mahesh and T. P. Murali, Thermal expansion in various phases of Nitinol using TMA, Physica B, 270 (1999), 289-297.
doi: 10.1016/S0921-4526(99)00186-6.
|
[71]
|
J. Wang, Z. Moumni, W. Zhang, Y. Xu and W. Zaki, A 3D finite-strain-based constitutive model for shape memory alloys accounting for thermomechanical coupling and martensite reorientation, Smart Mater. Struct., 26 (2017), 065006.
doi: 10.1088/1361-665X/aa6c17.
|
[72]
|
W. Zaki and Z. Moumni, A three-dimensional model of the thermomechanical behavior of shape memory alloys, J. Mech. Phys. Solids, 55 (2007), 2455-2490.
doi: 10.1016/j.jmps.2007.03.012.
|
[73]
|
X. Zhang, P. Feng, Y. He, T. Yu and Q. Sun, Experimental study on rate dependence of macroscopic domain and stress hysteresis in niti shape memory alloy strips, Int. J. Mech. Sci., 52 (2010), 1660-1670.
doi: 10.1016/j.ijmecsci.2010.08.007.
|