Nonlinear Electroelastic Deformations

Dorfmann, Luis; Ogden, Ray W.

doi:10.1007/s10659-005-9028-y

Cited by 191 publications

(152 citation statements)

References 17 publications

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“…Alternatively, equation (3) can be presented in a spatial setting in terms of the Eulerian electric displacement field D, defined as D 0 = H T D [11,12]. Analogously, the local form of the static Faraday law and its associated boundary conditions can be written as…”

Section: Gauss and Faraday Lawsmentioning

confidence: 99%

“…In equation (4b), ∂ ϕ V ⊂ ∂V represents the part of the boundary subjected to electric potential boundary conditions, such that ∂ ω V ∪ ∂ ϕ V = ∂V and ∂ ω V ∩ ∂ ϕ V = ∅. Equations (4) could alternatively be presented in a spatial or Eulerian setting in terms of the Eulerian electric field E, related to its Lagrangian counterpart E 0 via the standard relationship E 0 = F T E [11,12].…”

Section: Gauss and Faraday Lawsmentioning

confidence: 99%

“…For isotropic materials, the isochoric component of the extended internal energy W is typically represented [11,12,15] …”

Section: Convexification (Stabilisation) Of Materially Unstable Invarmentioning

confidence: 99%

“…Several authors [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] have contributed to the development of a well established variational framework for the numerical simulation of electro active materials. Crucial to this variational framework is the definition of well posed constitutive equations, as these materials are prone to develop a variety of electromechanical instabilities [25].…”

Section: Introductionmentioning

confidence: 99%

“…Once all the elements of the set V exact have been determined, it is possible to obtain the set of exact work conjugates Σ exact V via equation (12). Moreover, the hydrostatic pressure associated to the constitutive model in equation (75) for the smooth displacement field in equation (77) is obtained as…”

mentioning

confidence: 99%

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A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Ortigosa

Gil

Lee

2016

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: R. Ortigosa, A.J. Gil, C.H. Lee, A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies, Comput. Methods Appl. Mech. Engrg. (2016), http://dx.doi.org/10. 1016/j.cma.2016.06.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies. AbstractThe series of papers published by Gil and Ortigosa [1-3] introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Reference [1] in the context of compressible electro-elasticity, a novel extended Hu-Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-

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Section: Gauss and Faraday Lawsmentioning

confidence: 99%

Section: Gauss and Faraday Lawsmentioning

confidence: 99%

“…For isotropic materials, the isochoric component of the extended internal energy W is typically represented [11,12,15] …”

Section: Convexification (Stabilisation) Of Materially Unstable Invarmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Ortigosa

Gil

Lee

2016

Computer Methods in Applied Mechanics and Engineering

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Electrical Properties of Polymers

Riande

Díaz‐Calleja

2013

Handbook of Measurement in Science and Engineering

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The physics underlying the response of condensed matter to static and alternating electric force fields is briefly described. The relation between polarization and static electric fields leading to the estimation of the dipole moments of isolated polymer chains is progressively developed. Attention is paid to the dependence of the polarity of polymer chains on their chemical structure. The variation of the complex dielectric permittivity with the frequency of the perturbing electric field is studied at several temperatures above and below the glass transition temperature of polymers. It is shown that only in the case that the dipole moment scales with chains length, the dielectric relaxation spectra exhibits at low frequencies the normal mode relaxation arising from chains disentanglements. Relaxation spectra of polymers are profoundly affected by the development of order in these systems. The structures that make polymers suitable to be used as semiconductors, electronic and ionic conductors as well as actuators, are described. Moreover, the usefulness and performance of polymers in these endeavors are discussed. Finally, comments are made on the electrical breakdown in electrical isolating polymers.

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Computational structural and material stability analysis in finite electro‐elasto‐statics of electro‐active materials

Miehé

Vallicotti

Zäh

2015

Numerical Meth Engineering

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SUMMARYDielectric materials like electro-active polymers (EAPs) exhibit coupled electro-mechanical behavior at large strains. They respond by a deformation to an applied electrical field and are used in advanced industrial environments as sensors and actuators, for example, in robotics, biomimetics and smart structures. In fieldactivated or electronic EAPs, the electric activation is driven by Coulomb-type electrostatic forces, resulting in Maxwell stresses. These materials are able to provide finite actuation strains, which can even be improved by optimizing their composite microstructure. However, EAPs suffer from different types of instabilities. This concerns global structural instabilities, such as buckling and wrinkling of EAP devices, as well as local material instabilities, such as limit-points and bifurcation-points in the constitutive response, which induce snap-through and fine scale localization of local states. In this work, we outline variational-based definitions for structural and material stability, and design algorithms for accompanying stability checks in typical finite element computations. The formulation starts from stability criteria for a canonical energy minimization principle of electro-elasto-statics, and then shifts them over to representations related to an enthalpy-based saddle point principle that is considered as the most convenient setting for numerical implementation. Here, global structural stability is analyzed based on a perturbation of the total electro-mechanical energy, and related to statements of positive definiteness of incremental finite element tangent arrays. We base the local material stability on an incremental quasi-convexity condition of the electro-mechanical energy, inducing the positive definiteness of both the incremental electro-mechanical moduli as well as a generalized acoustic tensor. It is shown that the incremental arrays to be analyzed in the stability criteria appear within the enthalpy-based setting in a distinct diagonal form, with pure mechanical and pure electrical partitions. Applications of accompanying stability analyses in finite element computations are demonstrated by means of representative model problems.

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Nonlinear Electroelastic Deformations

Cited by 191 publications

References 17 publications

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Electrical Properties of Polymers

Computational structural and material stability analysis in finite electro‐elasto‐statics of electro‐active materials

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