Research Articles

A Solid Shell Finite Element Formulation for Dielectric Elastomers

[+] Author and Article Information
Sven Klinkel

Baustatik und Baudynamik,
Department of Civil Engineering,
RWTH Aachen University,
D-52056 Aachen, Germany
e-mail: sven.klinkel@bauing.uni-kl.de

Sandro Zwecker

Statik und Dynamik der Tragwerke,
Department of Civil Engineering,
TU Kaiserslautern,
D-67653 Kaiserslautern, Germany

Ralf Müller

Technische Mechanik,
Department of Mechanical &
Process Engineering,
TU Kaiserslautern,
D-67653 Kaiserslautern, Germany

Manuscript received May 24, 2012; final manuscript received August 2, 2012; accepted manuscript posted August 23, 2012; published online January 30, 2013. Assoc. Editor: Chad Landis.

J. Appl. Mech 80(2), 021026 (Jan 30, 2013) (11 pages) Paper No: JAM-12-1204; doi: 10.1115/1.4007435 History: Received May 24, 2012; Revised August 02, 2012; Accepted August 23, 2012

This paper is concerned with a solid shell finite element formulation to simulate the behavior of thin dielectric elastomer structures. Dielectric elastomers belong to the group of electroactive polymers. Due to efficient electromechanical coupling and the huge actuation strain, they are very interesting for actuator applications. The coupling effect in the material is mainly caused by polarization. In the present work, a simple constitutive relation, which is based on an elastic model involving one additional material constant to describe the polarization state, is incorporated in a solid shell formulation. It is based on a mixed variational principle of Hu-Washizu type. Thus, for quasi-stationary fields, the balance of linear momentum and Gauss' law are fulfilled in a weak sense. As independent fields, the displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements are employed. The element has eight nodes with four nodal degrees of freedom, three mechanical displacements, and the electric potential. The surface oriented shell element models the bottom and the top surfaces of a thin structure. This allows for a simple modeling of layered structures by stacking the elements through the thickness. Some examples are presented to demonstrate the ability of the proposed formulation.

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Fig. 1

The reference and the current configuration with position vectors X→ and x→, respectively

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Fig. 2

Hexahedral element with collocation points for assumed natural strain interpolations

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Fig. 3

Geometrical data and loading of the structure

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Fig. 4

Finite element mesh with 1 element, regular mesh

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Fig. 5

Finite element mesh with 64 elements, regular mesh

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Fig. 6

Finite element mesh with 5 elements, irregular mesh

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Fig. 7

Compression strain (%) in thickness direction versus the applied voltage at point A

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Fig. 8

Deformed configuration with a plot of the displacement in the x-direction

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Fig. 9

Plate with hole: geometry and finite element model

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Fig. 10

Relationship between voltage and displacement at point A

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Fig. 11

Residual norm of the 1st and 2nd loadstep

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Fig. 12

Deformed configuration with a plot of the displacement in the y-direction

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Fig. 13

Bending actuator: geometry

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Fig. 14

Deformed configurations with a color plot of the applied voltage

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Fig. 15

Dimensions of the peristaltic pump actuator

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Fig. 16

Loading of the tube actuator: three zones are loaded separately

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Fig. 17

Deformed configuration: at the 127. Load step zone 2 is fully loaded.

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Fig. 18

Dimensions of one layer of the buckling pump actuator

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Fig. 19

Load deflection curve of the buckling device

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Fig. 20

Buckling actuator: deformed device at φ = 125 V with an opening of 1.4 mm



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