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Discrete approximation of dynamic phase-field fracture in visco-elastic materials
An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys
1. | Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, CZ-186 75 Praha 8, Czech Republic |
2. | Institute of Thermomechanics, Czech Academy of Sciences, Dolejškova 5, CZ-182 00 Praha 8, Czech Republic |
3. | Institute of Physics, Czech Acad. Sci., Prague, Czech Republic, Na Slovance, CZ-18121 Praha 8, Czech Republic |
4. | Faculty of Nuclear Sciences and Physical Engineering, Czech Tech. Univ., Trojanova 13, CZ-120 00 Praha 2, Czech Republic |
A phenomenological model for polycrystalline NiTi shape-memory alloys with a refined dissipation function is here enhanced by a thermomechanical coupling and rigorously analyzed as far as existence of weak solutions and numerical stability and convergence of the numerical approximation performed by a staggered time discretization. Moreover, the model is verified on one-dimensional computational simulations compared with real laboratory experiments on a NiTi wire.
References:
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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.
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J. Arghavani, F. Auricchio, R. Naghdabadi, A. Reali and S. Sohrabpour,
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|
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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. |
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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.
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F. Auricchio, D. Fugazza and R. Desroches,
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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.
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Nonlocal integral formulations of plasticity and damage: Survey of progress, J. Eng. Mech., 128 (2002), 1119-1149.
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Micro-to-meso scale limit for shape-memory-alloy models with thermal coupling, Multiscale Model. Simul, 10 (2012), 1059-1089.
doi: 10.1137/110852176. |
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Mobility of twin and phase boundaries, J. de Physique IV, 112 (2003), 163-166.
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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. |
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A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loading, Eur. J. Mech. A, 23 (2004), 37-61.
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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. |
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Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation, Mech. Mater., 43 (2011), 361-376.
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doi: 10.2514/6.2015-1509. |
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P. Colli,
Global existence for the three-dimensional Frémond model of shape memory alloys, Nonlinear Analysis, Th. Meth. Appl., 24 (1995), 1565-1579.
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P. Colli, M. Frémond and A. Visintin,
Thermo-mechanical evolution of shape memory alloys, Quarterly Appl. Math., 48 (1990), 31-47.
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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.
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Thermodynamic extremal principles for irreversible processes in materials science, Acta Mater., 67 (2014), 1-20.
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A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations, Math. Mech. Solids, 21 (2016), 358-382.
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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).
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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.
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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.
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show all references
References:
[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,
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[1] | [kPa |
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[ |
[ |
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[ |
[ |
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[ |
[W/(m |
Parameter | Value | Unit | Parameter | Value | Unit |
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[mm] | [mm] | |||
[1] | [GPa] | ||||
[GPa] | [GPa] | ||||
[MPa/ |
[MPa] | ||||
[MPa] | [kPa/ |
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[1] | [kPa |
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[ |
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