Effective Behavior of Dielectric Elastomer Composites

Citation

Tian, Lixiu (2008) Effective Behavior of Dielectric Elastomer Composites. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CZNF-JB47. https://resolver.caltech.edu/CaltechETD:etd-08272007-145455

Abstract

The class of electroactive polymers has been developed to a point where real life applications as ``artificial muscles" are conceivable. These actuator materials provide attractive advantages: they are soft, lightweight, can undergo large deformation, possess fast response time and are resilient. However, widespread application has been hindered by their limitations: the need for a large electric field, relatively small forces and energy density. However, recent experimental work shows great promise that this limitation can be overcome by making composites of two materials with high contrast in their dielectric modulus. In this thesis, a theoretical framework is derived to describe the electrostatic effect of the dielectric elastomers. Numerical experiments are conducted to explain the reason for the promising experimental results and to explore better microstructures of the composites to enhance the favorable properties.

The starting point of this thesis is a general variational principle, which characterizes the behavior of solids under combined mechanical and electrical loads. Based on this variational principle, we assume the electric field is small as of order ε½, assume further the deformation is caused by the electrostatic effects; the deformation field is then of order ε. Using the tool of Γ-convergence, we derive a small-strain model in which the electric field and the deformation field are decoupled which results in a huge simplification of the problem.

Based on this small-strain model, employing the powerful tool of two-scale convergence, we derive the effective properties for dielectric composites conducting small strains. A formula of the effective electromechanical coupling coefficients is given in terms of the unit cell solutions.

Armed with these theoretical results, we carry out numerical experiments about the effective properties of different kind of composites. A very careful analysis of the numerical results provides a deep understanding of the mechanism of the enhancement in strain by making composites of different microstructures.

Thesis Files