Incremental Magnetoelastic Deformations, with Application to Surface Instability

Otténio, Melanie; Destrade, Michel; Ogden, Ray W.

doi:10.1007/s10659-007-9120-6

Cited by 64 publications

(72 citation statements)

References 25 publications

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“…This requires an appropriate formulation of the governing equations that can be used as a basis for the derivation of the incremental equations. In the static context of magnetoelasticity the Lagrangian formulation of the equations enabled the incremental equations to be obtained in a relatively simple form [43]; these were then applied to the analysis of surface instability of a half-space. The corresponding analysis for electroelasticity was given in [44].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…For magnetoelasticity the first and third of these were obtained by Otténio et al [43], wherein different notation was use for C 0ij|k . For electroelasticity the first and second were given by Dorfmann and Ogden [44], with different notation for B 0ij|k .…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…Explicit expressions for the derivatives of the invariants appearing above are listed in the appendix of [43] and are not repeated here. For an incompressible material these expressions remain in force except that I 3 ≡ 1 and the derivatives of Ω with respect to I 3 are omitted in the summations.…”

Section: Isotropic Magnetoelasticitymentioning

confidence: 99%

“…Note the distinction between μ(0) and μ 0 , the latter, we recall, being the magnetic permeability of free space. In slightly different notation this model was used in Otténio et al [43], wherein the interpretation of the coupling constants was discussed.…”

Section: Example: a Prototype Magnetoelastic Solidmentioning

confidence: 99%

“…where we have introduced the notations For an isotropic material, for a pure homogeneous strain aligned with the coordinate axes, with B 1 = 0, and for the purely static situation, equations (145) and (146) reduce to equations obtained by Otténio et al [43], in which case δ = = a = c = g = 0. The notation used here is different from that in the latter paper.…”

Section: Two-dimensional Specializationmentioning

confidence: 99%

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Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ogden¹

2009

International Journal of Non-Linear Mechanics

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The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.

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Section: Accepted Manuscriptmentioning

confidence: 99%

Section: Accepted Manuscriptmentioning

confidence: 99%

Section: Isotropic Magnetoelasticitymentioning

confidence: 99%

Section: Example: a Prototype Magnetoelastic Solidmentioning

confidence: 99%

Section: Two-dimensional Specializationmentioning

confidence: 99%

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Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Ogden¹

2009

International Journal of Non-Linear Mechanics

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A multiscale approach to the computational characterization of magnetorheological elastomers

Keip

Rambausek

2016

Numerical Meth Engineering

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Summary Magnetorheological elastomers are materials with a composite microstructure that consists of an elastomeric matrix and magnetizable inclusions. Because of the magnetic inclusions, magnetorheological elastomers are able to change their properties under magnetic field. Thereby, their effective behavior strongly depends on the microstructure. This calls for homogenization strategies to characterize their macroscopic response. However, for arbitrary macroscopic bodies, this is a non‐trivial task. The main difficulty stems from the fact that a magnetic body interacts with its surrounding and thus perturbs the magnetic field it is subjected to. In a multiscale simulation, this interaction has to be accounted for through a physically sound prescription of magnetic boundary conditions. Thus, the goal of this contribution is to establish a two‐scale homogenization framework that allows for both (i) the incorporation of the microstructure into the macroscopic simulation and (ii) the application of experimentally motivated boundary conditions on arbitrary macroscopic bodies. We show the capabilities of the approach in several numerical studies, in which we analyze the effective behavior of different specimens. Depending on their microstructure, we observe a contraction or extension of the specimens and find magnetically induced stiffening or weakening. All numerical predictions are in good qualitative agreement with experimental measurements. Copyright © 2016 John Wiley & Sons, Ltd.

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Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

Pelteret

Davydov

McBride

et al. 2016

Numerical Meth Engineering

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(2016) Computational electro-and magneto-elasticity for quasi-incompressible media immersed in free space. International Journal for Numerical Methods in Engineering, 108(11), pp. 1307-1342.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. This is the peer reviewed version of the following article: Pelteret, J. SUMMARYIn this work a mixed variational formulation to simulate quasi-incompressible electro-or magnetoactive polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.

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Incremental Magnetoelastic Deformations, with Application to Surface Instability

Cited by 64 publications

References 25 publications

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

A multiscale approach to the computational characterization of magnetorheological elastomers

Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

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