The effect of an exterior electric field on the instability of dielectric plates

Su, Yipin; Chen, Weiqiu; Dorfmann, Luis; Destrade, Michel

doi:10.1098/rspa.2020.0267

Cited by 9 publications

(4 citation statements)

References 43 publications

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“…The authors pointed out that the numerical results of Díaz-Calleja [112] do not reveal an extensional mode of wrinkling and seem to present numerical instabilities. Later, this work [43] was extended by Su et al [114] to examine the effect of exterior electric fields. In the work by Dorfmann and Ogden [115], the Stroh method was developed for analyzing the bifurcation of DE plates.…”

Section: Platementioning

confidence: 99%

“…In the work by Dorfmann and Ogden [115], the Stroh method was developed for analyzing the bifurcation of DE plates. Unlike the previous works [43,46,113,114], the material constitutive law was given in terms of the energy function Ω * (F, D L ). Explicit bifurcation equations were obtained for antisymmetric and symmetric modes of bifurcation, and the results were illustrated for a Gent electroelastic material model with different values of the Gent parameter.…”

Section: Platementioning

confidence: 99%

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Electromechanical Deformations and Bifurcations in Soft Dielectrics: A Review

Su,

Shen,

Zhao

et al. 2024

Materials

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Dielectric elastomers have attracted considerable attention both from academia and industry alike over the last two decades due to their superior mechanical properties. In parallel, research on the mechanical properties of dielectrics has been steadily advancing, including the theoretical, experimental, and numerical aspects. It has been recognized that the electromechanical coupling property of dielectric materials can be utilized to drive deformations in functional devices in a more controllable and intelligent manner. This paper reviews recent advances in the theory of dielectrics, with specific attention focused on the theory proposed by Dorfmann and Ogden. Additionally, we provide examples illustrating the application of this theory to analyze the electromechanical deformations and the associated bifurcations in soft dielectrics. We compared the bifurcations in elastic and dielectric materials and found that only compressive bifurcation modes exist in elastic structures, whereas both compressive and tensile modes coexist in dielectric structures. We summarize two proposed ways to suppress and prevent the tensile bifurcations in dielectric materials. We hope that this literature survey will foster further advancements in the field of the electroelastic theory of soft dielectrics.

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Section: Platementioning

confidence: 99%

Section: Platementioning

confidence: 99%

Electromechanical Deformations and Bifurcations in Soft Dielectrics: A Review

Su,

Shen,

Zhao

et al. 2024

Materials

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“…The third and final problem, Figure 1(c), consists of the elastomer deforming (and floating) in vacuum between two electrodes held at a fixed distance L, as first studied by Diaz-Calleja et al [18] (the vacuum can be also substituted by an ideal fluid, in that case the permittivity should be adjusted). Su et al [32] also examined the instability of a dielectric slab floating in a conductive fluid undergoing equi-biaxial deformation. In all cases, the elastomer is deformed homogeneously in plane-strain conditions from a thickness d 0 to d (fringing effects are neglected); therefore,…”

Section: Three Electroelastic Problems For a Thin Elastomermentioning

confidence: 99%

Surface instabilities of soft dielectric elastomers with implementation of electrode stiffness

Liguori

Gei

2022

Mathematics and Mechanics of Solids

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This paper contains a thorough investigation into plane-strain electroelastic surface instabilities of dielectric elastomers. We employ a systematic approach to our investigation, introducing three ways to actuate an elastomer device, namely, actuation by means of (1) attached compliant electrodes, (2) sprayed charges onto the opposite surfaces, and (3) fixed electrodes between which the device “floats” in vacuum and expands transversally. We examine electromechanical instability with particular attention to the third listed mode of actuation and the features of the specimen. We then tackle surface instability for the three modes, showing the relationship between applied pre-stress and the stability domain, as well as the characteristics of the obtained bifurcation fields. The effects of the stiffness of the electrode (relevant in the first listed mode of actuation) on surface instabilities are then investigated by adopting an elastic surface–substrate interaction model in which the properties of the coating enter the boundary conditions for the substrate. Various electrode materials are assumed, demonstrating that their implementation in the model increases the number of solutions at bifurcation and changes the overall stability domain. We present this new enriched bifurcation map, showing the dependence on the wavenumber, and characterise the solutions by examining the bifurcated fields.

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“…These assumptions ensure that the field heterogeneity is only confined to the plate edges, while far away from the edges, the induced stress and magnetic field distributions can be envisioned as uniform, which is a good approximation in the sense of Saint-Venant's principle. A similar processing method has been adopted by Su et al (2020) to analyze the wrinkling of soft electro-active plates immersed in external electric fields.…”

Section: Pure Homogeneous Deformation Of a Platementioning

confidence: 99%

Wrinkling of soft magneto-active plates

Destrade

2021

International Journal of Solids and Structures

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Coupled magneto-mechanical wrinkling has appeared in many scenarios of engineering and biology. Hence, soft magneto-active (SMA) plates buckle when subject to critical uniform magnetic field normal to their wide surface. Here, we provide a systematic analysis of the wrinkling of SMA plates subject to an in-plane mechanical load and a transverse magnetic field. We consider two loading modes: plane-strain loading and uni-axial loading, and two models of magneto-sensitive plates: the neo-Hookean ideal magneto-elastic model and the neo-Hookean magnetization saturation Langevin model. Our analysis relies on the theory of nonlinear magneto-elasticity and the associated linearized theory for superimposed perturbations. We derive the Stroh formulation of the governing equations of wrinkling, and combine it with the surface impedance method to obtain explicitly the bifurcation equations identifying the onset of symmetric and antisymmetric wrinkles. We also obtain analytical expressions of instability in the thin-and thick-plate limits. For thin plates, we make the link with classical Euler buckling solutions. We also perform an exhaustive numerical analysis to elucidate the effects of loading mode, load amplitude, and saturation magnetization on the nonlinear static response and bifurcation diagrams. We find that antisymmetric wrinkling modes always occur before symmetric modes. Increasing the pre-compression or heightening the magnetic field has a destabilizing effect for SMA plates, while the saturation magnetization enhances their stability. We show that the Euler buckling solutions are a good approximation to the exact bifurcation curves for thin plates.

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The effect of an exterior electric field on the instability of dielectric plates

Cited by 9 publications

References 43 publications

Electromechanical Deformations and Bifurcations in Soft Dielectrics: A Review

Electromechanical Deformations and Bifurcations in Soft Dielectrics: A Review

Surface instabilities of soft dielectric elastomers with implementation of electrode stiffness

Wrinkling of soft magneto-active plates

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