Two- and three-dimensional modeling approaches in magneto-mechanics: a quantitative comparison

Metsch, Philipp; Kalina, Karl A.; Brummund, Jörg; Kästner, Markus

doi:10.1007/s00419-018-1442-2

Cited by 28 publications

(43 citation statements)

References 52 publications

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“…The magnetic part of the coupled problem requires Maxwells equations to be solved [ 55 ]. Assuming a material body which is free of any current densities and surface currents, they are given by

and their associated jump conditions [ 56 ]. Here,

and

represent the magnetic induction as well as the magnetic field of a material point in the current configuration [ 57 ]—they are linked by the magnetization

via the equation

with

being the permeability of free space.…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…Here,

and

represent the magnetic induction as well as the magnetic field of a material point in the current configuration [ 57 ]—they are linked by the magnetization

via the equation

with

being the permeability of free space. As shown in [ 56 , 57 ], the coupling of the mechanical fields into the magnetic equations can be pointed out by defining the reference fields using the deformation gradient

and its determinant J :

…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…Therein,

is the first Piola–Kirchhof stress tensor. Within the FE simulations, the fulfillment of the condition is ensured by making use of representative volume elements (RVEs) for which periodic boundary conditions are applied [ 56 ].…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…As can be seen from the results for the cubic microstructure in Figure 4 a, a field-induced stiffening is found for all particle-volume fractions

. All curves show the typical behavior of an initially quadratic course with a saturation for higher magnetic fields [ 56 , 69 ]. Qualitatively, the results are in good agreement with findings of other authors [ 70 , 71 ].…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

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Magneto-Mechanical Coupling in Magneto-Active Elastomers

et al. 2021

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In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle–interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures.

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“…The magnetic part of the coupled problem requires Maxwells equations to be solved [ 55 ]. Assuming a material body which is free of any current densities and surface currents, they are given by

and their associated jump conditions [ 56 ]. Here,

and

represent the magnetic induction as well as the magnetic field of a material point in the current configuration [ 57 ]—they are linked by the magnetization

via the equation

with

being the permeability of free space.…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…Here,

and

represent the magnetic induction as well as the magnetic field of a material point in the current configuration [ 57 ]—they are linked by the magnetization

via the equation

with

and its determinant J :

…”

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…Therein,

Section: Micro-modeling Strategiesmentioning

confidence: 99%

“…As can be seen from the results for the cubic microstructure in Figure 4 a, a field-induced stiffening is found for all particle-volume fractions

Section: Micro-modeling Strategiesmentioning

confidence: 99%

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Magneto-Mechanical Coupling in Magneto-Active Elastomers

et al. 2021

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“…Exemplary for modern theoretical developments, we mention the works of Kovetz, Dorfmann and Ogden, Kankanala and Triantafyllidis, McMeeking and Landis, Ericksen and Suo et al The references cited earlier are concerned with a continuum perspective irrespective of scale. Magnetorheological elastomers, however, require to account for microstructural effects and macrostructural effects at the same time. While in the case of MREs, continuum theories can be applied on both scales, the scale bridging or homogenization is another central aspect when dealing with these microheterogeneous materials.…”

Section: Introductionmentioning

confidence: 99%

A two‐scale FE‐FFT approach to nonlinear magneto‐elasticity

Rambausek

Göküzüm

Nguyen

et al. 2018

Numerical Meth Engineering

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Fourier-based approaches are a well-established class of methods for the theoretical and computational characterization of microheterogeneous materials.Driven by the advent of computational homogenization techniques, Fourier schemes gained additional momentum over the past decade. In recent contributions, the interpretation of Green operators central to Fourier solvers as projections opened up a new perspective. Based on such a viewpoint, the present work addresses a multiscale framework for magneto-mechanically coupled materials at finite strains. The key ingredient for the solution of magneto-mechanic boundary value problems at the microscale is the construction of suitable operators in Fourier space that project vector fields onto either curl-free or divergence-free subspaces. The resulting linear system of equations is solved by a conjugate gradient method. In addition to that, we describe the computation of the consistent macroscopic tangent operator based on the same linear operators as the microscopic equilibrium with appropriately defined right-hand sides. We employ the framework for the simulation of representative two-scale boundary value problems and compare the results with pure finite element schemes.

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The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Saber

2023

Adv Eng Mater

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The magnetorheological elastomers (MREs) are novel multifunctional materials wherein their viscoelastic properties can be varied instantly under an application of applied magnetic field. Due to their field‐dependent stiffness and damping properties, MREs are widely used in the development and design of MRE‐based adaptive vibration isolators and absorbers and also biomedical engineering. Moreover, MREs due to their inherent magnetostriction effect have enormous potential for the development of soft actuators. The dynamic behavior of MREs is affected by various material parameters (e.g., matrix and particle types, particle concentration, additives) as well as mechanical and magnetic loading parameters (e.g., frequency, amplitude, temperature, magnetic flux density). Understanding and predicting the effect of materials and loading parameters on the response behavior of MREs are of paramount importance for the design of MRE‐based adaptive structures and systems. This review paper mainly aims to provide a comprehensive study of material constitutive models to predict the nonlinear magnetomechanical behavior of MREs. Particular emphasis is paid to physics‐based models including continuum‐ and microstructure‐based models. Moreover, phenomenological models describing the dynamic magnetoviscoelastic behavior of MREs as well as the effect of temperature on the magnetomechanical behavior of such materials are properly addressed.

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Two- and three-dimensional modeling approaches in magneto-mechanics: a quantitative comparison

Cited by 28 publications

References 52 publications

Magneto-Mechanical Coupling in Magneto-Active Elastomers

Magneto-Mechanical Coupling in Magneto-Active Elastomers

A two‐scale FE‐FFT approach to nonlinear magneto‐elasticity

The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

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