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

This paper presents a three-dimensional phenomenological constitutive model for magnetic shape memory alloys (MSMAs), developed within the framework of irreversible continuum thermodynamics. To this end, a proper set of internal variables is introduced to reflect the microstructural consequences on the material macroscopic behavior. Moreover, a stress-dependent thermodynamic force threshold for variant reorientation is introduced which improves the model accuracy. Preassumed kinetic equations for magnetic domain volume fractions, decoupled equations for magnetization unit vectors and appropriate presentation of the limit function for martensite variant reorientation lead to a simple formulation of the proposed constitutive model. To show the model capability in reproducing the main features of MSMAs, several numerical examples are solved and compared with available experimental data as well as available three-dimensional constitutive models in the literature. Demonstrating good agreement with experimental data besides possessing computational advantages, the proposed constitutive model can be used for analysis of MSMA-based smart structures.

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“…We refer the reader to Haldar and Lagoudas [26] where they discuss the single crystal anisotropic behavior.…”

Section: ( )mentioning

confidence: 99%

A three-dimensional constitutive model for magnetic shape memory alloys under magneto-mechanical loadings

Mousavi

Arghavani

2016

Smart Mater. Struct.

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“…The permeability of the free space is μ 0 , and the density of the material is ρ. A detailed discussion on the construction of the Gibbs free potential for MSMAs and constitutive responses, including discrete crystalline symmetry restrictions, could be found in [15,31]. We further consider the evolution equations for the reorientation strain and the mixing energy as…”

Section: (A) Magnetic Shape Memory Alloy Constitutive Responsesmentioning

confidence: 99%

“…In the reorientation mechanism, the variants have different preferred directions of magnetization and the magnetic field is applied to select certain variants, which results in the macroscopic shape change. We follow Haldar & Lagoudas [15] among the many other available modelling approaches which aim to capture the phenomenology of the material responses.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system

Haldar

Lagoudas

2020

Proc. R. Soc. A.

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Magnetic shape memory alloys (MSMAs) have drawn significant research attention as potential high actuation energy multi-functional materials. Such a dissipative material system can be considered as a solid continuum interacting with a magnetic field. A continuum-based phenomenological model provides a magneto-mechanical system of equations that simulates and predicts primary MSMA behaviours. In this work, we investigate the local symmetries of the MSMA system equations through the Lie group analysis. Symmetry breaking due to stable-unstable transition is analysed. The conservation laws are derived, and their physical meaning is scrutinized.

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“…3 Elaborate experimental methods are needed to analyze coupled multi-field e↵ects and, therefore, such studies are rarely reported in the literature. [6][7][8][9] Multi-field property measurements are increasingly sought after to understand the coupled material behaviors 3 and to calibrate constitutive models, [10][11][12][13][14] and thereby improve the active material response.…”

Section: Introductionmentioning

confidence: 99%

High-field magneto-thermo-mechanical testing system for characterizing multiferroic bulk alloys

Bruno

Караман

Ross

et al. 2015

Review of Scientific Instruments

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Multiferroic meta-magnetic shape memory alloys are well known for exhibiting large magnetic field induced actuation strains, giant magnetocaloric effects, magneto-resistance, and structural and magnetic glassy behaviors. Thus, they are candidates for improving modern day sensing, actuation, magneto-resistance, and solid-state refrigeration processes. Until now, however, experimental apparatuses have typically been able to probe a limited ferroic parameter space in these materials, i.e., only concurrent thermal and mechanical responses, or magnetic and thermal responses. To overcome this barrier and better understand the coupling of multiple fields on materials behavior, a magneto-thermo-mechanical characterization device has been designed and implemented. This device is capable of compressing a specimen at load levels up to 5300 N collinearly with applied fields up to 9 T between temperatures of -100 °C and 120 °C. Uniaxial stress, strain, temperature, magnetic field, and the volumetric average magnetization have been simultaneously measured under mixed loading conditions on a NiCoMnIn meta-magnetic shape memory alloy and a few selected results are presented here.

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

Cited by 9 publications

References 52 publications

A three-dimensional constitutive model for magnetic shape memory alloys under magneto-mechanical loadings

A three-dimensional constitutive model for magnetic shape memory alloys under magneto-mechanical loadings

Lie symmetry and conservation laws for magneto-static magnetic shape memory alloys system

High-field magneto-thermo-mechanical testing system for characterizing multiferroic bulk alloys

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