Magnetoelasticity of highly deformable thin films: Theory and simulation

Barham, Matthew; Steigmann, David J.; White, Dan

doi:10.1016/j.ijnonlinmec.2011.05.004

Cited by 26 publications

(11 citation statements)

References 29 publications

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“…This hypothesis is also supported theoretically by the work of Barham et al [32] in the case of magnetoelasticity, when the magnetic field is connected with a scalar potential and the general three-dimensional problem is reduced to twodimensions through a membrane approximation. The second hypothesis (no boundary surface free space electric energy) states that the purely electric part of the free energy is only due to the free space and is not affected by surface electricity, which is exclusively due to the material nature of the boundary surface.…”

Section: Electric Behaviour Of Bodies With Energetic Surfacementioning

confidence: 56%

Surface electrostatics: theory and computations

2014

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The objective of this work is to study the electrostatic response of materials accounting for boundary surfaces with their own (electrostatic) constitutive behaviour. The electric response of materials with (electrostatic) energetic boundary surfaces (surfaces that possess material properties and constitutive structures different from those of the bulk) is formulated in a consistent manner using a variational framework. The forces and moments that appear due to bulk and surface electric fields are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress and the Maxwell stress is examined.

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Section: Electric Behaviour Of Bodies With Energetic Surfacementioning

confidence: 56%

Surface electrostatics: theory and computations

2014

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“…Quantum mechanical considerations and molecular dynamics simulations in respect of polarized lipid membranes [Seelig 1978;Frischleder and Peinel 1982;Warshaviak et al 2011] indicate that the polarization vector is essentially tangential to the film surface. In this case an estimate based on (5) -derived in the mathematically identical context of magnetostatics [Barham et al 2012]indicates that the magnitude |e s | of the self field is of order O(t ln t); for small t this is negligible compared to unity. It follows that the leading-order energy, i.e., the limit of E/t as t → 0, is given by (18) but with W simplified to…”

Section: Liquid Crystal Filmsmentioning

confidence: 99%

Untitled

2016

Math. Mech. Compl. Sys.

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The concept of internal constraints is extended to gradient materials. Here, interesting constraints can be introduced, such as pseudorigid ones. The stresses and the hyperstresses will be given by constitutive equations only up to reactive parts, which do no work during any compatible motion of the body. For the inclusion of thermodynamical effects, the theory is generalized to the case of thermomechanical constraints. Here one obtains reactive parts of the stresses, heat flux, entropy, and energy, which do not contribute to the dissipation. Some critical remarks on the classical concept of internal constraints are finally given. A method to introduce internal constraints in a natural way is described to overcome some conceptual deficiencies of the classical concept.Communicated by Francesco dell'Isola. MSC2010: 74A30. 1 2 ALBRECHT BERTRAM AND RAINER GLÜGE format. It turns out, and will be shown in the sequel, that such an extension is in fact straightforward once a theory of gradient materials has been constructedat least within the mechanical context.The extension to a thermomechanical format is more complicated. This is, however, necessary not only in order to investigate the compatibility of such constraints with the second law of thermodynamics, but also to study the temperature dependence of mechanical constraints.There has been some discussion about a sound format for the inclusion of the thermodynamical variables into such a theory of internal constraints; see [Green et al. ].The starting point for the present approach is a suggestion by [Trapp 1971; Bertram 2005], where a rate form of a thermomechanical constraint is assumed and the possibility for reactive parts of the stresses, heat fluxes, and energies is given that are not dissipative during any process that is compatible with the constraint. Again, the extension of this theory to gradient materials is straightforward.At the end of this contribution, some critical remarks on the standard theory of mechanical constraints are given and a procedure to avoid these shortcomings is suggested.Dedicated to Gérard Maugin, in gratitude for many years of inspiration and friendshipThe differential-geometric underpinnings of a unified theory of material uniformity and evolution are exposed in terms of the language of groupoids subordinate to geometric distributions. Both the standard theory of material uniformity and the extended theory of functionally graded materials are included in the formulation as well as their temporal counterparts in anelastic and aging processes.In this paper we reinvestigate the structure of the solution of a well-known Love's problem, related to the electrostatic field generated by two circular coaxial conducting disks, in terms of orthogonal polynomial expansions, enlightening the role of the recently introduced class of the Lucas-Lehmer polynomials. Moreover we show that the solution can be expanded more conveniently with respect to a Riesz basis obtained starting from Chebyshev polynomials.This paper deals with the modeling of cy...

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“…In the present paper we shall not make use of M, but we remark that equation (5) gives an explicit expression for M in terms of either H or B as the independent variable when B (respectively H) is given in terms of H (respectively B) by a constitutive law. The magnetization itself is also often used as the independent magnetic variable, as, for example, in the work of Kankanala and Triantafyllidis [3].…”

Section: The Equations Of Magnetostatics: Eulerian Formmentioning

confidence: 99%

“…Recent years have seen an increasing interest in studying theoretically the behaviour of a class of smart materials called magnetosensitive (MS) elastomers; see, for example, the works by Dorfmann and Ogden [1,2], Kankanala and Triantafyllidis [3] and Steigmann and co-workers [4,5]. 1 MS elastomers can exhibit large nonlinear elastic deformations when subjected to external magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear magnetoelastostatics: Energy functionals and their second variations

Bustamante

Ogden

2012

Mathematics and Mechanics of Solids

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Artículo de publicación ISITwo variational principles for nonlinear magnetoelastostatics are studied, considering a magnetosensitive body completely surrounded by free space extending to infinity. The functionals depend on the deformation function as one of the independent variables, and on either the scalar magnetic potential or the magnetic vector potential as the independent magnetic variable. Alternative representations for the energy densities are given for free space, from which simple expressions for the first and second variations of the functionals are obtained

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Magnetoelasticity of highly deformable thin films: Theory and simulation

Cited by 26 publications

References 29 publications

Surface electrostatics: theory and computations

Surface electrostatics: theory and computations

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Nonlinear magnetoelastostatics: Energy functionals and their second variations

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