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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-014-0403-4