Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response

Smart Materials and Structures

Volumn 21, Issue 9, 2012, Pages

  Kiefer, B ^a   Bartel, T ^a   Menzel, A ^a,b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED FORM SOLUTIONS; FULLY-COUPLED; INTERNAL VARIABLES; MAGNETIC SHAPE MEMORY ALLOYS; MARTENSITIC VARIANTS; NEWTON-RAPHSON; NUMERICAL INTEGRATION SCHEME; NUMERICAL INTEGRATIONS; NUMERICAL SOLUTION; OPTIMIZATION PROBLEMS; RETURN MAPPING ALGORITHM; STRAIN EVOLUTION;

CONFORMAL MAPPING; CONSTRAINED OPTIMIZATION; FUNCTIONS; SHAPE MEMORY EFFECT;

LOADING;

EID: 84866118851     PISSN: 09641726     EISSN: 1361665X     Source Type: Journal    
DOI: 10.1088/0964-1726/21/9/094007     Document Type: Article

References (38)

1. Kiefer B and Lagoudas D C 2005 Magnetic field-induced martensitic variant reorientation in magnetic shape memory alloys Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289329 (Pubitemid 43149136)
2. Kiefer B and Lagoudas D C 2009 Modeling the coupled strain and magnetization response of magnetic shape memory alloys under magnetomechanical loading J. Intell. Mater. Syst. Struct. 20 14370
3. 2MnGa single crystals Appl. Phys. Lett. 69 19668 (Pubitemid 126619270)
4. OHandley R C 1998 Model for strain and magnetization in magnetic shape-memory alloys J. Appl. Phys. 83 326370
5. James R D and Wuttig M 1998 Magnetostriction of martensite Phil. Mag. A 77 127399 (Pubitemid 128358519)
6. James R D and Hane K F 2000 Martensitic transformations and shape-memory materials Acta Mater. 48 197222 (Pubitemid 30558403)
7. Likhachev A A and Ullakko K 2000 Magnetic-field-controlled twin boundaries motion and giant magneto-mechanical effects in NiMnGa shape memory alloy Phys. Lett. A 275 14251
8. Hirsinger L and Lexcellent C 2003 Modelling detwinning of martensite platelets under magnetic and (or) stress actions on nimnga alloys J. Magn. Magn. Mater. 254/255 2757 (Pubitemid 35437427)
9. DeSimone A 2004 Coarse-grained models of materials with non-convex free-energy: two case studies Comput. Methods Appl. Mech. Eng. 193 512941 (Pubitemid 39499830)
10. Kiefer B 2006 A phenomenological constitutive model for magnetic shape memory alloys Ph D Dissertation Department of Aerospace Engineering, Texas A & M University, College Station, TX
11. Kiang J and Tong L 2005 Modelling of magneto-mechanical behavior of NiMnGa single crystals J. Magn. Magn. Mater. 292 394412 (Pubitemid 40423127)
12. Morrison P, Seelecke S, Krevet B and Kohl M 2008 A free energy model for magneto-mechanically coupled NiMnGa single crystals Eur. Phys. J. - Spec. Top. 158 21320
13. Krevet B and Kohl M 2010 Thermodynamic modelling of ferromagnetic shape memory actuators Mater. Sci. Forum 635 17580
14. Stefanelli U 2012 Magnetic control of magnetic shape-memory single crystals Physica B 407 131621
15. Stefanelli U and Bessoud A-L 2011 Magnetic shape memory alloys: three-dimensional modeling and analysis Math. Models Methods Appl. Sci. 21 104369
16. Auricchio F, Bessoud A-L, Reali A and Stefanelli U 2011 A three-dimensional phenomenological model for magnetic shape memory alloys GAMM-Mitteilungen 34 906
17. Landis C M 2008 A continuum thermodynamics formulation for micro-magnetomechanics with applications to ferromagnetic shape memory alloys J. Mech. Phys. Solids 56 305976
18. Jin Y M 2009 Domain microstructure evolution in magnetic shape memory alloys: phase-field model and simulation Acta Mater. 57 248895
19. Mennerich C, Wendler F, Jainta M and Nestler B 2011 A phase-field model for the magnetic shape memory effect Arch. Mech. 63 184575
20. Conti S, Lenz M and Rumpf M 2007 Modeling and simulation of magnetic-shape-memory polymer composites J. Mech. Phys. Solids 55 146286 (Pubitemid 46719250)
21. Ge Y, Heczko O, Söderberg O and Lindroos V K 2004 Various magnetic domain structures in NiMnGa martensite exhibiting magnetic shape memory effect J. Appl. Phys. 96 215963
22. Sullivan M R and Chopra H D 2004 Temperature- and field-dependent evolution of micromagnetic structure in ferromagnetic shape-memory-alloys Phys. Rev. B 70 094427
23. Miehe C, Kiefer B and Rosato D 2011 An incremental variational formulation of dissipative magnetostriction at the macroscopic continuum level Int. J. Solids Struct. 48 184666
24. Miehe C, Rosato D and Kiefer B 2011 Variational principles in dissipative electro-magneto-mechanics: a framework for the macro-modeling of functional materials Int. J. Numer. Methods Eng. 86 122576
25. Truesdell C and Toupin R 1960 The classical field theories Principles of Classical Mechanics and Field Theory (Encyclopedia of Physics vol III/1) ed S Flügge (Berlin: Springer) pp 226795
26. Simo J C and Hughes T J R 1998 Computational Inelasticity (Interdisciplinary Applied Mathematics vol 7) (New York: Springer)
27. Qidwai M A and Lagoudas D C 2000 Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms Int. J. Numer. Eng. 47 112368 (Pubitemid 30542454)
28. Lagoudas D C 2008 Introduction to Modeling and Engineering Applications of Shape Memory Alloys (New York: Springer)
29. Hartl D J, Chatzigeorgiou G and Lagoudas D C 2010 Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys Int. J. Plast. 26 1485507
30. Jayabal K, Menzel A, Arockiarajan A and Srinivasan S M 2011 Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach Comput. Mech. 48 42135
31. Fischer A 1992 A special Newton-type optimization method Optimization 24 26984
32. Schmidt-Baldassari M 2003 Numerical concepts for rate-independent single crystal plasticity Comput. Methods Appl. Mech. Eng. 192 126180 (Pubitemid 36333621)
33. Bartel T and Hackl K 2009 A micromechanical model for martensitic phase-transformations in shape-memory alloys based on energy-relaxation Z. Angew. Math. Mech. 89 792809
34. Bartel T and Hackl K 2010 Multiscale modeling of martensitic phase transformations: on the numerical determination of heterogeneous mesostructures within shape-memory alloys induced by precipitates Techn. Mech. 30 32442
35. Bartel T, Menzel A and Svendsen B 2011 Thermodynamic and relaxation-based modeling of the interaction between martensitic phase transformations and plasticity J. Mech. Phys. Solids 59 100419
36. Miehe C 1996 Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity Comput. Methods Appl. Mech. Eng. 134 22340 (Pubitemid 126393654)
37. Scheday G 2003 Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmemethoden Dissertation Universität Stuttgart
38. Menzel A, Arockiarajan A and Sivakumar S M 2008 Two models to simulate rate-dependent domain switching effects - application to ferroelastic polycrystalline ceramics Smart Mater. Struct. 17 015026