Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers

Keip, Marc‐André; Rambausek, Matthias

doi:10.1016/j.ijsolstr.2017.04.012

Cited by 66 publications

(42 citation statements)

References 67 publications

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“…As shown in Fig. In case of a rectangular shaped sample, this effect intensifies [2,3]. In case of a rectangular shaped sample, this effect intensifies [2,3].…”

Section: Resultsmentioning

confidence: 88%

“…1(c), the induced magnetization within the sample is almost homogeneous, whereas the deformation field is strongly inhomogeneous. In case of a rectangular shaped sample, this effect intensifies [2,3]. This demonstrates again, that the parameter identification for macroscopic MRE models from experimental results requires several assumptions in the fitting process.…”

Section: Resultsmentioning

confidence: 97%

“…Finally a circular MRE sample within a surrounding free space is simulated, where special attention is drawn to the magnetostriction [3,4], i. e. the elongation or contraction in an external field h ∞ . As shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Due to the inhomogeneous fields inside the MRE sample [2,3], this procedure however requires several simplifying assumptions. In the former, the heterogeneous microstructure is explicitly resolved and it is possible to predict the effective behavior of the composite.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Development of a Macro‐Model for Magnetorheological Elastomers based on Microscopic Simulations

Kalina

Metsch

Brummund

et al. 2019

Proc Appl Math and Mech

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Herein, the parametrization of a macro-model for magneto-rheological elastomers based on microscopic simulations is presented. Within a computational homogenization, the effective response of the composite system is calculated and the data are used for parameter identification. The merit of this strategy is the adjustment of the model independent of any macroscopic sample geometry. With the developed model, the magnetostrictive behavior of a macroscopic sample is simulated.

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“…As shown in Fig. In case of a rectangular shaped sample, this effect intensifies [2,3]. In case of a rectangular shaped sample, this effect intensifies [2,3].…”

Section: Resultsmentioning

confidence: 88%

Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Development of a Macro‐Model for Magnetorheological Elastomers based on Microscopic Simulations

Kalina

Metsch

Brummund

et al. 2019

Proc Appl Math and Mech

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“…This example analyses the behavior of a chain of ferromagnetic particles under the influence of an applied external magnetic field h. The influence of the particle distribution on the overall deformation of the MRE has been reported in literature [2,3]. Two chains of iron particles embedded in an elastomeric matrix are considered here, with different distribution of the iron particles as shown in Fig.1.…”

Section: Numerical Examplementioning

confidence: 99%

A Large‐Deformation Phase‐Field Approach for the Modeling of Magneto‐Sensitive Elastomers

Sridhar

Keip

Miehé

2017

Proc Appl Math and Mech

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Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magnetomechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1,7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. Primary variables in finite-deformation micro-magneto-elasticityThe macroscopic boundary-value-problem for a ferromagnetic body B embedded in free space Ω is a coupled multifield problem. Primary variables are the deformation map ϕ, the scalar magnetic potential φ and the reference magnetization director M given by,Note that the magnetization director is a priori defined only in the ferromagnetic material and has the geometric property M ∈ S d−1 , where S d−1 is the space of a unit sphere. The magnetization director and its rate in terms of the spin of magnetization ω ∈ R d are given as,This geometric property has to be consistently taken into account in our formulation. The magnetization of the material has a fixed value m s , where m s is the spontaneous magnetization of the material. The deformation gradient directly follows from the deformation map as F = Gradϕ and the reference self magnetic field as H = −Grad φ. Penalty formulation for the unity constraint on the directorAs mentioned before the geometric property of the magnetization director |M | = 1 has to be consistently taken into account in the formulation. A numerical implementation of the exact update of the magnetization is given in [7] and a staggered solution scheme is presented in [1]. A pure penalty formulation has been presented in [6], for small deformations. We propose here a staggered penalty solution scheme to satisfy this constraint. To this end the unity constraint on the magnetization director is relaxe...

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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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Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers

Cited by 66 publications

References 67 publications

Development of a Macro‐Model for Magnetorheological Elastomers based on Microscopic Simulations

Development of a Macro‐Model for Magnetorheological Elastomers based on Microscopic Simulations

A Large‐Deformation Phase‐Field Approach for the Modeling of Magneto‐Sensitive Elastomers

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

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