Computational modeling of electro-elasto-capillary phenomena in dielectric elastomers
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Dielectric Elastomers (DEs) based have significant potential in the emerging field of soft actuators and soft robotics. Due to the highly non-linear electromechanical coupling, DEs can easily undergo large deformation and electromechanical instabilities when subject to an external potential. The deformation and instabilities can cause failures often detrimental in various application of DEs, though they can also be systematically harnessed to create enhanced functionalities such as dynamic surface patterning, and energy harvesting. In recent years DEs have been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and reliability. While an excellent literature already exists for electromechanical instabilities, it is still unknown how the effects of surface tension and elasto-capillary forces coupled with electromechanical forces to impact the modes of instabilities on DEs. Furthermore, all available computational models for DEs are monolithically coupled, which are extremely computationally inefficient, and place stringent limits on the DE system sizes that can be modeled. In this thesis, a finite element method (FEM) model is developed to capture surface tension effects on DEs, a phenomena called electro-elasto-capillary (EEC) phenomena. The finite element formulation is dynamic, non-linear, monolithic, and fully coupled. This model is capable of capturing both the onset of instabilities as well as the post-instability response of DEs. The model is used to examine the following problems of interest: (1) Surface tension-driven surface instability transition from creasing to wrinkling in constrained DE films; (2) Wrinkling instability in pre-compressed DEs subjected to surface tension; (3) Occurrence of an electro-elasto-capillary Rayleigh-Plateau instability (RPI) in DE films; (4) Bursting drops inside a DE film. In the second focus of this thesis, a new staggered explicit-implicit FEM model is developed, which offers significant enhancement in computational efficiency while maintaining numerical robustness and solution accuracy compared to the fully coupled and monolithic model. Comparisons to the monolithic solutions for the above-mentioned problems of interest are given, while three-dimensional problems which cannot be solved monolithically are tackled using the proposed explicit-implicit formulation.
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