Abstract
In this paper, we present a complete direct approach to nonlinear modeling of thin plates, which are made of incompressible dielectric elastomers. In particular, the dielectric elastomers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of electrostatic forces is incorporated by the purely electrical contribution to the augmented Helmholtz free energy. Our approach does not involve any extraction-type procedure from the three-dimensional energy to derive the plate augmented free energy, but directly postulates the form of this energy for the structural plate problem treated in this paper. Results computed within the framework of this novel approach are compared to results available in the literature as well as to our own three-dimensional finite element solutions. A very good agreement is found.
Highlights
The present paper is dedicated to the memory of Vladimir Vasilyevich Eliseev and his pioneering work on modern versions of the linear and nonlinear theories for thin elastic rods, plates and shells, for which he developed geometrically nonlinear equations in a compact tensorial form based on the principle of virtual work applied to material lines and surfaces
We extend the direct approach for elastic shells he presented in [6] and that was further developed by Vetyukov [7] to the case of electro-active plates modeled as electro-elastic material surfaces
We discuss the governing equations of a thin plate modeled as a two-dimensional electro-elastic material surface with mechanical and electrical degrees of freedom
Summary
The present paper is dedicated to the memory of Vladimir Vasilyevich Eliseev and his pioneering work on modern versions of the linear and nonlinear theories for thin elastic rods, plates and shells, for which he developed geometrically nonlinear equations in a compact tensorial form based on the principle of virtual work applied to material lines and surfaces. A practically important sub-class of electro-active polymers are dielectric elastomers, which are rubber-type materials that exhibit a polarization when an external electric field is applied at electrodes mounted to its top and bottom surfaces. By this polarization, the electrodes get attracted due to the corresponding electrostatic forces, such that the resulting squeezing yields large in-plane deformations.
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