Finite element analysis of the demagnetization effect and stress inhomogeneities in magnetic shape memory alloy samples

Haldar, Krishnendu; Kiefer, Björn; Lagoudas, Dimitris C.

doi:10.1080/14786435.2011.602031

Cited by 44 publications

(41 citation statements)

References 58 publications

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“…In order to give a comprehensive description on the magneto-mechanical response of a MSMA specimen, one also needs to solve the coupled PDE system composed of the constitutive equations and the magnetic and mechanical field equations. In the literature, several works have been reported on the numerical implementation of this coupled PDE system [20,21].…”

Section: Introductionmentioning

confidence: 99%

“…In some phase field models [26,27], the demagnetization energy is incorporated to study the variations of variant state and magnetization vector at the microscopic level. In [21], a non-linear magnetostatic problem is solved by using the finite element method, based on which the demagnetization effect on the responses of MSMA specimens is addressed in detail. The average demagnetization field in the specimen is calculated through both the finite element analysis and the simplified demagnetization factor considerations.…”

Section: Introductionmentioning

confidence: 99%

“…In some other models [10][11][12][18][19][20][21], the crystallographic feature and the magnetic domain structure of MSMA materials are taken into account. Several internal variables are adopted to represent the coexistence of different variants and magnetic domains in MSMA specimens.…”

Section: Introductionmentioning

confidence: 99%

“…consider one twin interface or one material point) in some of the existing models could not be sufficient to predict the global response of a MSMAspecimen, because some important factors, for example, the shape and size of the MSMA specimen, the variant distribution in the specimen, the demagnetization field in the surrounding space, are not taken into account. In the literature, the demagnetization effect has been studied in several modelling works [20,21,24,26,27,30]. For example, DeSimone [24] considered a MSMA sample with an ellipsoid shape, in which the demagnetization field is calculated based on the average magnetization and a demagnetizing tensor.…”

Section: Introductionmentioning

confidence: 99%

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Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Wang

Steinmann

2013

Philosophical Magazine

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In this paper, the stress-and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account. A typical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions obtained in this model can predict the response of the MSMA sample at a quantitative level.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Wang

Steinmann

2013

Philosophical Magazine

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“…-The intensity of multi-field coupling may be high. The influence of magnetic field on stress has been reported to be more than 15% compared with the stress level under a no field condition by solving a simplified magneto-mechanical boundary value problem for MSMA [49].…”

Section: (B) Continuous Symmetry and Field-induced Phase Transformationmentioning

confidence: 99%

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

Haldar

Lagoudas

2014

Proc. R. Soc. A.

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A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

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Numerical energy relaxation to model microstructure evolution in functional magnetic materials

2015

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This paper proposes energy relaxation‐based approaches for the modeling of magnetostriction, with a particular focus on single crystalline magnetic shape memory alloy response. The theoretical development relies on concepts of energy relaxation in the context of nonconvex free energy landscapes whose wells define preferred states of spontaneous straining and magnetization. The constrained theory of magnetoelasticity developed by DeSimone and James [1] represents the point of departure for the model development, and its capabilities, but also limitations, are demonstrated by means of representative numerical examples. The key features that characterize the extended approach are (i) the incorporation of elastic deformations, whose distribution among the individual phases occurs in an energy minimizing fashion, (ii) a finite magnetocrystalline anisotropy energy, that allows magnetization rotations away from easy axes, and (iii) dissipative effects, that are accounted for in an incremental variational setting for standard dissipative materials. In the context of introducing elastic strain energy, two different relaxation concepts, the convexification approach and the rank‐one relaxation with respect to first‐order laminates, are considered. In this manner, important additional response features, e.g. the hysteretic nature, the linear magnetization response in the pre‐variant reorientation regime, and the stress dependence of the maximum field induced strain, can be captured, which are prohibited by the inherent assumptions of the constrained theory. The enhanced modeling capabilities of the extended approach are demonstrated by several representative response simulations and comparison to experimental results taken from literature. These examples particularly focus on the response of single crystals under cyclic magnetic field loading at constant stress and cyclic mechanical loading at constant magnetic field. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Finite element analysis of the demagnetization effect and stress inhomogeneities in magnetic shape memory alloy samples

Cited by 44 publications

References 58 publications

Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

Numerical energy relaxation to model microstructure evolution in functional magnetic materials

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