Nonlinear magnetoelastic deformations of elastomers

Dorfmann, Luis; Ogden, Ray W.

doi:10.1007/s00707-003-0061-2

Cited by 175 publications

(173 citation statements)

References 10 publications

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“…The continuity condition across a surface of discontinuity in the current configuration is of the form [37][38][39] τ n =t + τ m n, (2.8) where ift is the mechanical traction per unit area, and τ m is the Maxwell stress due to the magnetic field outside the material near the boundary of the body [56] …”

Section: (Grad B)mentioning

confidence: 99%

“…Many of these works have been influenced by the different theories on electroelasticity, which were developed earlier (see [78] and the review in §3(a) in [4]). In all these works as well as several others that we will cite later, the main assumption has been to express the stress tensor (either the total stress tensor or other definitions for it [37,38,58] in the case of bodies with memory) of the strains, 4 i.e. expressions of the form:…”

Section: Constitutive Relations In Classical Linear and Nonlinear Magmentioning

confidence: 99%

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Implicit constitutive relations for nonlinear magnetoelastic bodies

Bustamante

Rajagopal

2015

Proc. R. Soc. A.

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Implicit constitutive relations that characterize the response of elastic bodies have greatly enhanced the arsenal available at the disposal of the analyst working in the field of elasticity. This class of models were recently extended to describe electroelastic bodies by the present authors. In this paper, we extend the development of implicit constitutive relations to describe the behaviour of elastic bodies that respond to magnetic stimuli. The models that are developed provide a rational way to describe phenomena that have hitherto not been adequately described by the classical models that are in place. After developing implicit constitutive relations for magnetoelastic bodies undergoing large deformations, we consider the linearization of the models within the context of small displacement gradients. We then use the linearized model to describe experimentally observed phenomena which the classical linearized magnetoelastic models are incapable of doing. We also solve several boundary value problems within the context of the models that are developed: extension and shear of a slab, and radial inflation and extension of a cylinder.

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Section: (Grad B)mentioning

confidence: 99%

Section: Constitutive Relations In Classical Linear and Nonlinear Magmentioning

confidence: 99%

Implicit constitutive relations for nonlinear magnetoelastic bodies

Bustamante

Rajagopal

2015

Proc. R. Soc. A.

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“…Based on the classical laws of elasticity, electricity and magnetism, the general equations have been derived and several boundary-value problems have been solved [7][8][9][10][11][12][13]. In particular, for magnetorheological elastomers, modeling efforts have been presented recently [14][15][16][17][18]. In these efforts the magnetorheological elastomer is examined in a macroscopic level and general magnetomechanical laws are presented.…”

Section: Introductionmentioning

confidence: 99%

Unified magnetomechanical homogenization framework with application to magnetorheological elastomers

Chatzigeorgiou

Javili

Steinmann

2012

Mathematics and Mechanics of Solids

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The aim of this work is to present a general homogenization framework with application to magnetorheological elastomers under large deformation processes. The macroscale and microscale magnetomechanical responses of the composite in the material and spatial description are presented and the conditions for a well-established homogenization problem in Lagrangian description are identified. The connection between the macroscopic magnetomechanical field variables and the volume averaging of the corresponding microscopic variables in the Eulerian description is examined for several types of boundary conditions. It is shown that the use of kinematic and magnetic field potentials instead of kinetic field and magnetic induction potentials provides a more appropriate homogenization process.

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“…There is considerable current interest among mechanicians in nonlinear magnetoelasticity [1][2][3][4][5]. This is due to the development of highly deformable magnetizable materials synthesized from elastomers infused with micro-or nano-scopic ferrous particles [6].…”

Section: Introductionmentioning

confidence: 99%

Magnetoelasticity of highly deformable thin films: Theory and simulation

Barham¹,

Steigmann²,

White³

2012

International Journal of Non-Linear Mechanics

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A nonlinear two-dimensional theory is developed for thin magnetoelastic films capable of large deformations. This is derived directly from the three-dimensional theory. Significant simplifications emerge in the descent from three dimensions to two, permitting the self field generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers and numerical solutions are obtained to equilibrium boundaryvalue problems in which the membrane is subjected to lateral pressure and an applied magnetic field.

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Nonlinear magnetoelastic deformations of elastomers

Cited by 175 publications

References 10 publications

Implicit constitutive relations for nonlinear magnetoelastic bodies

Implicit constitutive relations for nonlinear magnetoelastic bodies

Unified magnetomechanical homogenization framework with application to magnetorheological elastomers

Magnetoelasticity of highly deformable thin films: Theory and simulation

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