In this article, we present a nonlinear theory for thin plates, which are made of incompressible electroded dielectric elastomer layers. The layers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of the electrostatic forces is taken into account by means of the electrostatic stress tensor. A plane state of stress is imposed on the total stress tensor, based on which two-dimensional constitutive relations for the plate are derived. A geometrically nonlinear formulation for the plate as a material surface is devloped, and solutions are computed using nonlinear finite elements. The numerical results are compared to available results from the literature verifying our approach, and an additional nonsymmetric example problem is studied with respect to stability.
We present a novel multistage hybrid asymptotic-direct approach to the modeling of the nonlinear behavior of thin shells with piezoelectric patches or layers, which is formulated in a holistic form for the first time in this paper. The key points of the approach are as follows: (1) the asymptotic reduction in the threedimensional linear theory of piezoelasticity for a thin plate; (2) a direct approach to geometrically nonlinear piezoelectric shells as material surfaces, which is justified and completed by demanding the mathematical equivalence of its linearized form with the asymptotic solution for a plate; and (3) the numerical analysis by means of an FE scheme based on the developed model of the reduced electromechanically coupled continuum. Our approach is illustrated by examples of static and steady-state analysis and verified with three-dimensional solutions computed with the commercially available FE code ABAQUS as well as by comparison with results reported in the literature.
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