Magnetoelastic modelling of elastomers

Dorfmann, Luis; Ogden, Ray W.

doi:10.1016/s0997-7538(03)00067-6

Cited by 247 publications

(199 citation statements)

References 7 publications

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“…These classical theories have been used in the recent years to account for large deformations and nonlinear magneto-mechanical interaction in order to study magnetoelastic polymers. Brigadnov and Dorfmann (2003), and Dorfmann and Ogden (2003) proposed a formulation based on a total free energy density that is a function of deformation and the magnetic flux density. It was later shown by Dorfmann and Ogden (2005) that magnetic field or magnetization vector can also be used as an independent variable in the same formulation.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Limit points in the free inflation of a magnetoelastic toroidal membrane

Reddy

Saxena

2017

International Journal of Non-Linear Mechanics

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“…(1)), it then exhibits a O(1/ ) asymptotic behavior whenever microscale variations of the type x/ are present. In this sense, our formulation considers locally unbounded body forces, which are regular and well-defined in the context of the elastic problem (8)(9)(10)(11)(12), nonetheless asymptotically behaving as 1/ when representation (15) holds. The systems of PDEs (8-12) turns out to be homogenizable assuming microscale periodicity, as done in the rest of this work.…”

Section: The Asymptotic Homogenization Techniquementioning

confidence: 99%

Effective balance equations for elastic composites subject to inhomogeneous potentials

Penta

Ramírez-Torres

Merodio

et al. 2017

Continuum Mech. Thermodyn.

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We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and non-standard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.

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“…Equilibria of this system are precisely the unique solutions to (109) and (115) 1 . Further, solutions to this system satisfy the energy balances…”

Section: Lyapunov Functionsmentioning

confidence: 99%

“…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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Magnetoelastic modelling of elastomers

Cited by 247 publications

References 7 publications

Limit points in the free inflation of a magnetoelastic toroidal membrane

Limit points in the free inflation of a magnetoelastic toroidal membrane

Effective balance equations for elastic composites subject to inhomogeneous potentials

Magnetoelasticity of highly deformable thin films: Theory and simulation

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