On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm

This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has...

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Published in:	Continuum mechanics and thermodynamics Vol. 28; no. 3; pp. 669 - 698
Main Authors:	Wang, Jiong, Steinmann, Paul
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2016 Springer Springer Nature B.V
Subjects:	Algorithms Alloys Classical and Continuum Physics Computer simulation Continuum mechanics Crystallization Demagnetization Engineering Thermodynamics Heat and Mass Transfer Magnetic fields Magnetism Magnetization Mathematical models Numerical analysis Original Article Physics Physics and Astronomy Shape memory alloys Structural Materials Theoretical and Applied Mechanics Three dimensional Finite element method Twin interface Iterative numerical algorithm Magnetic shape memory alloys Configurational force
ISSN:	0935-1175, 1432-0959
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Abstract	This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.
AbstractList	This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated. This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample's response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated. Keywords Magnetic shape memory alloys * Twin interface * Configurational force * Finite element method * Iterative numerical algorithm
Audience	Academic
Author	Wang, Jiong Steinmann, Paul
Author_xml	– sequence: 1 givenname: Jiong surname: Wang fullname: Wang, Jiong email: ctjwang@scut.edu.cn organization: School of Civil Engineering and Transportation, South China University of Technology – sequence: 2 givenname: Paul surname: Steinmann fullname: Steinmann, Paul organization: Chair of Applied Mechanics, University of Erlangen-Nuremberg
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CitedBy_id	crossref_primary_10_1063_1_5115486 crossref_primary_10_1016_j_jallcom_2020_153940 crossref_primary_10_1080_14786435_2021_2012290 crossref_primary_10_1016_j_jmps_2021_104761 crossref_primary_10_1016_j_jmmm_2020_166650 crossref_primary_10_1063_5_0019615 crossref_primary_10_1016_j_jmps_2025_106272 crossref_primary_10_1007_s00161_015_0452_3 crossref_primary_10_1016_j_jmps_2023_105408 crossref_primary_10_1109_TMAG_2024_3404333 crossref_primary_10_1007_s00419_018_1482_7 crossref_primary_10_1007_s00707_022_03189_4
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Snippet	This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the...
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SubjectTerms	Algorithms Alloys Classical and Continuum Physics Computer simulation Continuum mechanics Crystallization Demagnetization Engineering Thermodynamics Heat and Mass Transfer Magnetic fields Magnetism Magnetization Mathematical models Numerical analysis Original Article Physics Physics and Astronomy Shape memory alloys Structural Materials Theoretical and Applied Mechanics Three dimensional
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Title	On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm
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