Nonlinear Theory of Electroelastic and Magnetoelastic Interactions

Dorfmann, Luis; Ogden, Ray W.

doi:10.1007/978-1-4614-9596-3

Cited by 164 publications

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“…It should be mentioned that the following derivations and analyses to describe the interaction between mechanical deformation and electric fields in DEs are not unique, and other theoretical frameworks exist and equivalently capture the electroelastic coupling in DEs. For example, Dorfmann and Ogden (2014) have developed a general theoretical framework, in the form of tensors, which applies for a broad range of electroactive and magnetoactive materials. In the following, we adopt the treatments more specific to DEs as being more consistent with the prevailing discussion on the topic.…”

Section: Basic Theory Of Desmentioning

confidence: 99%

Mechanics of dielectric elastomers: materials, structures, and devices

Qian

2016

JZUS-A

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Dielectric elastomers (DEs) respond to applied electric voltage with a surprisingly large deformation, showing a promising capability to generate actuation in mimicking natural muscles. A theoretical foundation of the mechanics of DEs is of crucial importance in designing DE-based structures and devices. In this review, we survey some recent theoretical and numerical efforts in exploring several aspects of electroactive materials, with emphases on the governing equations of electromechanical coupling, constitutive laws, viscoelastic behaviors, electromechanical instability as well as actuation applications. An overview of analytical models is provided based on the representative approach of non-equilibrium thermodynamics, with computational analyses being required in more generalized situations such as irregular shape, complex configuration, and time-dependent deformation. Theoretical efforts have been devoted to enhancing the working limits of DE actuators by avoiding electromechanical instability as well as electric breakdown, and pre-strains are shown to effectively avoid the two failure modes. These studies lay a solid foundation to facilitate the use of DE materials, structures, and devices in a wide range of applications such as biomedical devices, adaptive systems, robotics, energy harvesting, etc.

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Section: Basic Theory Of Desmentioning

confidence: 99%

Mechanics of dielectric elastomers: materials, structures, and devices

Qian

2016

JZUS-A

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“…Although the constitution of those materials is quite different, the mathematical formulation is very similar, for example, see the papers by Dorfmann and Ogden (2005), McMeeking and Landis (2005), and Castañeda and Siboni (2012). For an exhaustive survey on electro-and magneto-mechanics, we refer to the recent books on the subject by Ogden and Steigmann (2011), and Dorfmann and Ogden (2014).…”

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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“…Finally, in this section, we mention that different aspects of the theories discussed earlier and their applications are discussed in the texts by Landau & Lifshitz [118], which was restricted to the linearly elastic context, Nelson [103], Maugin [119], Eringen & Maugin [111], Hutter et al [109] and Dorfmann & Ogden [120].…”

Section: Continuum Theories Of Nonlinear Electromechanicsmentioning

confidence: 99%

“…for a derivation of which see [106] or [120]. We shall also make use of the density ρ F of free charges per unit volume in B r , which is defined by ρ F = Jρ f .…”

Section: (B) Lagrangian Formsmentioning

confidence: 99%

“…Note that E is denoted by E M in [2], which is the sum of the Maxwell self field and the external field. It is convenient in the present context to define the energy per unit reference volume and, as in [120], to use the polarization in the form ρ r π = JP, which we denote by P r (the polarization per unit reference volume). We write the energy, per unit reference volume, as U(F, P r ) = ρ r Σ (F, π), and the formulae in (7.1) can be recast as…”

Section: Function σ(F π) Defined Per Unit Mass In the Formmentioning

confidence: 99%

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Nonlinear electroelasticity: material properties, continuum theory and applications

Dorfmann

Ogden

2017

Proc. R. Soc. A.

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In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

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Nonlinear Theory of Electroelastic and Magnetoelastic Interactions

Cited by 164 publications

References 0 publications

Mechanics of dielectric elastomers: materials, structures, and devices

Mechanics of dielectric elastomers: materials, structures, and devices

Limit points in the free inflation of a magnetoelastic toroidal membrane

Nonlinear electroelasticity: material properties, continuum theory and applications

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