Abstract

The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo‐dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub‐iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo‐dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd. 

Abstract

Actuation devices made of dielectric elastomers are prone to compression induced wrinkling instabilities, which can adversely affect their performance and may lead to device failure. On the other hand, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. The idea of taut states and the natural width under simple tension plays an important role in the analysis of compression generated instability (wrinkling). In case of electrically driven DE membranes, the domain of taut states in the plane of principal stretches is influenced substantially by the applied voltage and the film's constitutive properties. In the recent past, there has been an increasing interest in exploiting anisotropy in the material behavior of dielectric elastomers for improving their actuation performance. Spurred with these ongoing efforts, this paper presents a continuum mechanics based electromechanical model for predicting the thresholds on the domain of taut states of transversely isotropic planar dielectric elastomers. The developed analytical framework uses an amended energy function that accounts for the electromechanical coupling for a class of incompressible transversely isotropic dielectric membranes. The required expressions for the total Cauchy stress tensor and the associated principal stress components are evaluated utilizing the amended energy function. Finally, the concept of natural width under simple tension is implemented to obtained the nonlinear coupled electromechanical equation that evaluates the associated taut states domain of the transversely isotropic planar dielectric elastomers. Our results indicate that the extent of taut domain can be controlled by modifying the level and the principal direction of the transverse isotropy. The taut states domain for a particular level of applied electric field increases with increase in the anisotropy parameter, while the taut domains depleted with the increase in fiber orientations from 00to 900for an applied level of electrical loading. The fiber-reinforced wrinkle-tunable surfaces can be effectively designed and developed using the underlying analytical framework and the trends obtained in this study.