Optimal energy-harvesting cycles for load-driven dielectric generators in plane strain

Roberta Springhetti, Eliana Bortot, Gal DeBotton, Massimiliano Gei

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


The performances of energy-harvesting generators based on dielectric elastomers are investigated. The configuration is that of a thin dielectric film coated by stretchable electrodes at both sides. The film is first stretched, then charged, afterwards it is released, and finally the charge is harvested at a higher electric potential. The amount of energy extracted by this cycle is bounded by the electric breakdown and the ultimate stretch ratio of the film, as well as by structural instabilities due to the loss of tension. To identify the optimal cycle that complies with these limits, we formulate a constraint optimization problem and solve it with a dedicated solver for two typical classes of elastic dielectrics. As anticipated, we find that the performance of the generator depends critically on the ultimate stretch ratio of the film. However, more surprising is our finding of a universal limit on the dielectric strength of the film beyond which the optimal cycle is independent of this parameter. Thus, we reveal that, regardless of how large the dielectric strength of the material is, there is an upper bound on the amount of harvested energy that depends only on the ultimate stretch ratio. We conclude the work with detailed calculations of the optimal cycles for two commercially available elastic dielectrics.

Original languageEnglish
Pages (from-to)929-946
Number of pages18
JournalIMA Journal of Applied Mathematics
Issue number5
StatePublished - 1 Oct 2014


  • Dielectric elastomers
  • Energy harvesting
  • Optimization
  • Smart materials

ASJC Scopus subject areas

  • Applied Mathematics


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