Dielectric elastomer composites: analytical and numerical non-convex homogenization methods and applications

Electroactive materials;Electrostriction;Microstructures;Iterated homogenization;Weighted essentially non-oscillatory (WENO) finite difference;Hamiton-Jacobi equation;Crouzeix–Raviart conforming elements

Lefevre, Victor

关键词: Electroactive materials;    Electrostriction;    Microstructures;    Iterated homogenization;    Weighted essentially non-oscillatory (WENO) finite difference;    Hamiton-Jacobi equation;    Crouzeix–Raviart conforming elements;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/98340/LEFEVRE-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

With the practical objective of shedding light on promising experimental results that have recently identified dielectric elastomer composites as potential enablers of new technologies (essentially, as the next generation of soft sensors and actuators), this work puts forth analytical and numerical methods to determine the macroscopic elastic dielectric behavior of this class of soft electroactive materials directly in terms of their microscopic behavior.The macroscopic behavior of dielectric elastomer composites is first investigated within the classical asymptotic context of small deformations and moderate electric fields. Specifically, by a combination of analytical and numerical techniques, rigorous homogenization solutions are constructed for dielectric elastomer composites with general (possibly anisotropic) classes of two-phase particulate microstructures. Aimed at identifying what types of filler particles lead to enhanced elastic dielectric behaviors, these solutions are deployed to examine dielectric elastomers filled with stiff high-permittivity particles, high-permittivity particles that are liquid-like in mechanical behavior, and vacuous pores.In addition to generalizing the fundamental purely elastic and purely dielectric solutions of Eshelby and Maxwell to the coupled and nonlinear realm of electroelastostatics, the above-outlined rigorous asymptotic solutions turn out to be essential in the development of corresponding homogenization solutions for finite deformations and finite electric fields. Indeed, it is shown that they can be utilized as building blocks for the derivation of a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. By construction, this approximate solution is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is assessed by direct comparisons with full-field hybrid finite-element simulations, as well as with numerical solutions generated via a new WENO finite-difference scheme developed specifically for this class of problems. With the object of scrutinizing recent experimental results, the specializations of the proposed solution to various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behaviors are discussed in detail.Stark disagreement between the theoretical results outlined above and a plurality of experimental results indicates that the basic point of view that dielectric elastomer composites can be idealized as two-phase particulate elastic dielectric composites is fundamentally incomplete, especially for cases involving stiff filler particles which (as opposed to what the theory predicts) have been reported to exhibit extreme enhancements in their electrostriction capabilities. It is posited that such extreme enhancements are the manifestation of interphasial phenomena. In particular, the presence of interphasial free charges that oscillate rapidly in space at the length scale of the microstructure of elastic dielectric composites is shown to have a significant and even dominant effect on their macroscopic response, possibly leading to extreme behaviors ranging from unusually large permittivities and electrostriction coefficients to metamaterial-type properties featuring negative permittivities. These results suggest a promising strategy to design deformable dielectric composites --- such as electrets and dielectric elastomer composites --- with exceptional electromechanical properties.