Nonlinear electroelastic deformations of dielectric elastomer composites: II — Non-Gaussian elastic dielectrics

Victor Lefèvre, Oscar Lopez-Pamies

Research output: Contribution to journalArticlepeer-review


This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response — under finite deformations and finite electric fields — of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method — this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics — to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

Original languageEnglish (US)
Pages (from-to)438-470
Number of pages33
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Feb 1 2017


  • Comparison medium methods
  • Crouzeix–Raviart conforming elements
  • Electroactive materials
  • Electrostriction
  • Microstructures

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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