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Mechanics of Advanced Materials and Structures Volume 13, 2006 - Issue 6
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Original Articles

Finite Element Analysis of Phase Transformation Dynamics in Shape Memory Alloys with a Consistent Landau-Ginzburg Free Energy Model

D. Roy Mahapatra Mathematical Modelling and Computational Sciences, Wilfrid Laurier University, Waterloo, ON, N2L3C5, Canada
&
R. V. N. Melnik Mathematical Modelling and Computational Sciences, Wilfrid Laurier University, Waterloo, ON, N2L3C5, Canada
Pages 443-455 | Received 26 Apr 2006, Published online: 24 Feb 2007

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Hossein Rahbar, Mahdi Javanbakht, Saeed Ziaei-Rad, Alessandro Reali & Hossein Jafarzadeh. (2022) Finite element analysis of coupled phase-field and thermoelasticity equations at large strains for martensitic phase transformations based on implicit and explicit time discretization schemes. Mechanics of Advanced Materials and Structures 29:17, pages 2531-2547.
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Ayedh Eid Alajmi, Talal Alsaeed, Jasem Ghanem Alotaibi, Jayanth Kumar Srelam & Belal F. Yousif. (2023) Investigating the lap shear adhesion of coir and glass-fibre reinforced epoxy bonding to mild steel with varying volume fractions. Frontiers in Mechanical Engineering 9.
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Mahdi Javanbakht, Hossein Rahbar & Milad Ashourian. (2019) Finite element implementation based on explicit, Galerkin and Crank–Nicolson methods to phase field theory for thermal- and surface- induced martensitic phase transformations. Continuum Mechanics and Thermodynamics 34:4, pages 935-953.
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W. M. Abd-Allah & Rasha Mohammad Fathy. (2022) Gamma irradiation effectuality on the antibacterial and bioactivity behavior of multicomponent borate glasses against methicillin-resistant Staphylococcus aureus (MRSA). JBIC Journal of Biological Inorganic Chemistry 27:1, pages 155-173.
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Xi Xie, Guozheng Kang, Qianhua Kan & Chao Yu. (2020) Phase-field theory based finite element simulation on thermo-mechanical cyclic deformation of polycrystalline super-elastic NiTi shape memory alloy. Computational Materials Science 184, pages 109899.
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Cheikh Cisse, Wael Zaki & Tarak Ben Zineb. (2016) A review of constitutive models and modeling techniques for shape memory alloys. International Journal of Plasticity 76, pages 244-284.
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R Dhote, M Fabrizio, R Melnik & J Zu. (2014) A three-dimensional non-isothermal Ginzburg–Landau phase-field model for shape memory alloys. Modelling and Simulation in Materials Science and Engineering 22:8, pages 085011.
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R. P. Dhote, R. N. V. Melnik & J. Zu. (2014) Dynamic multi-axial behavior of shape memory alloy nanowires with coupled thermo-mechanical phase-field models. Meccanica 49:7, pages 1561-1575.
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Hector Gomez, Alessandro Reali & Giancarlo Sangalli. (2014) Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models. Journal of Computational Physics 262, pages 153-171.
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Hui She, Yulan Liu, Biao Wang & Decai Ma. (2013) Finite element simulation of phase field model for nanoscale martensitic transformation. Computational Mechanics 52:4, pages 949-958.
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R.P. Dhote, M. Fabrizio, R.N.V. Melnik & J. Zu. (2013) Hysteresis phenomena in shape memory alloys by non-isothermal Ginzburg–Landau models. Communications in Nonlinear Science and Numerical Simulation 18:9, pages 2549-2561.
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Linxiang Wang & Roderick V.N. Melnik. (2012) Nonlinear dynamics of shape memory alloy oscillators in tuning structural vibration frequencies. Mechatronics 22:8, pages 1085-1096.
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Mirko Maraldi, Luisa Molari & Diego Grandi. (2012) A non-isothermal phase-field model for shape memory alloys: Numerical simulations of superelasticity and shape memory effect under stress-controlled conditions. Journal of Intelligent Material Systems and Structures 23:10, pages 1083-1092.
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Hector Gomez & Thomas J.R. Hughes. (2011) Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. Journal of Computational Physics 230:13, pages 5310-5327.
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F. Daghia, M. Fabrizio & D. Grandi. (2010) A non isothermal Ginzburg-Landau model for phase transitions in shape memory alloys. Meccanica 45:6, pages 797-807.
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Chetan S. Jarali & D. Roy Mahapatra. (2010) Modeling the interface effect of shape memory alloy composite materials. Multidiscipline Modeling in Materials and Structures 6:2, pages 257-283.
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Linxiang X. Wang & Roderick V. N. Melnik. (2010) Low Dimensional Approximations to Ferroelastic Dynamics and Hysteretic Behavior Due to Phase Transformations. Journal of Applied Mechanics 77:3.
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RODERICK V. N. MELNIK, XILIN WEI & GABRIEL MORENO–HAGELSIEB. (2011) NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS. Journal of Biological Systems 17:03, pages 425-460.
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Vikash K. Jha & D. Roy Mahapatra. (2009) Constitutive modeling of shape memory alloy wire with non-local rate kinetics. Continuum Mechanics and Thermodynamics 21:1, pages 1-15.
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Roderick V.N. Melnik. (2009) Coupling control and human factors in mathematical models of complex systems. Engineering Applications of Artificial Intelligence 22:3, pages 351-362.
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Bin Wen & Roderick Melnik. (2008) Relative stability of nanosized wurtzite and graphitic ZnO from density functional theory. Chemical Physics Letters 466:1-3, pages 84-87.
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