Finite deformation of a pressurized magnetoelastic membrane in a stationary dipole field

Barham, Matthew; Steigmann, David J.; McElfresh, M.; Rudd, Robert E.

doi:10.1007/s00707-007-0445-9

Cited by 29 publications

(45 citation statements)

References 17 publications

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“…Formulation presented here is based on the theory laid out in (Barham et al, 2007). The total potential energy (E) of a weakly magnetizable magnetoelastic membrane can be written as follows.…”

Section: Total Potential Energymentioning

confidence: 99%

“…where T is the undeformed membrane thickness, Ω represents the surface of the undeformed membrane, V 0 the enclosed initial volume and ∆V the change in the enclosed volume, ρ is the mass density, ψ(F, µ) is the free energy per unit mass defined in the formulation based on magnetization (Kankanala and Triantafyllidis, 2004;Barham et al, 2007),P is the gauge pressure of the inflating gas, µ is the material magnetization per unit mass, m = ρµ is the magnetization per unit current volume, µ 0 is the permeability of vacuum, and h a is the applied magnetic field. Note that the formulation here is based on the assumption that the self-generated magnetic field is negligible compared to the applied field.…”

Section: Total Potential Energymentioning

confidence: 99%

“…Cauchy stresses for the magnetoelastic incompressible material under consideration, according to Barham et al (2007) are as follows.σ…”

Section: Cauchy Stressesmentioning

confidence: 99%

“…They claim that magnetization per unit mass can be a better choice for an independent variable along with deformation gradient because, unlike magnetic flux or intensity, it vanishes outside the material. Their work (with magnetization as an independent variable in free energy density function) has later been utilised by Barham et al (2007Barham et al ( , 2008 for studying thin magnetoelastic membranes. We follow the same formulation in the current study.…”

Section: Introductionmentioning

confidence: 99%

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Limit points in the free inflation of a magnetoelastic toroidal membrane

Reddy

Saxena

2017

International Journal of Non-Linear Mechanics

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One common phenomenon native to inflation of membranes is the elastic limit-point instability-a bifurcation point at which the membrane begins to deform enormously at the slightest increase of pressure. In the case of magnetoelastic materials, there is another possible phenomenon which we call magnetic limitpoint instability, a state referring to the non-existence of an equilibrium state -either stable or unstable. In this work, we are concerned with such instabilities in an incompressible isotropic magnetoelastic toroidal membrane with an initial circular cross-section. A non-uniform magnetic field is generated using a circular current carrying loop placed inside the membrane in addition to inflation by a uniform hydrostatic pressure. An energy formulation based on magnetization is used to model the magneto-mechanical coupling along with a Mooney-Rivlin constitutive model for the elastic strain energy density. Computations show that the magnetic field strongly influences the location of elastic limit points and in some cases can cause them to vanish. Multiple equilibrium states are obtained as solutions of the governing equations and a criterion based on second variation is employed to determine their stability. Existence and dependence of magnetic limit point on the magnetic field is demonstrated. While the quantitative results obtained here are specific to the toroidal geometry, the deformation behaviour can be generalised to any magnetoelastic membrane.

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Section: Total Potential Energymentioning

confidence: 99%

Section: Total Potential Energymentioning

confidence: 99%

“…Cauchy stresses for the magnetoelastic incompressible material under consideration, according to Barham et al (2007) are as follows.σ…”

Section: Cauchy Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Limit points in the free inflation of a magnetoelastic toroidal membrane

Reddy

Saxena

2017

International Journal of Non-Linear Mechanics

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“…This property may be used to facilitate controlled pumping of fluid, for example, via remote actuation. In the present work we continue our development [7] of a membrane theory for thin films composed of such materials. This is used to simulate membrane response to an applied magnetic field and to a pressure transmitted to the material by a confined gas.…”

Section: Introductionmentioning

confidence: 74%

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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Oscillations of a magneto‐sensitive elastic sphere

Altenbach

Brigadnov²,

Eremeyev

2008

Z Angew Math Mech

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Magneto-sensitive (MS) or magnetorheological (MR) elastomers are smart materials whose mechanical properties change instantly by the application of a magnetic field. MS elastomers are widely used in the practice as elements of MEMS (sensors, actuators, etc.), for example, in medical devices. The behavior of MS elastomers under time-dependent magnetic field is a complex process and till now is not investigated in all details. Here we present the statements of the dynamic boundary-value problem of a MS elastomer and demonstrate the special features of the dynamic behavior of such system. As an example both the nonlinear and the linear oscillations of a MS elastic sphere are considered. The control of radially symmetric oscillations of MS elastic sphere by a homogeneous magnetic field is investigated. The presented results can be used for control and generation of radially symmetric acoustic waves using magnetic field excitation.

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Finite deformation of a pressurized magnetoelastic membrane in a stationary dipole field

Cited by 29 publications

References 17 publications

Limit points in the free inflation of a magnetoelastic toroidal membrane

Limit points in the free inflation of a magnetoelastic toroidal membrane

Magnetoelasticity of highly deformable thin films: Theory and simulation

Oscillations of a magneto‐sensitive elastic sphere

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