A blend of stretching and bending in nematic polymer networks

Olivier Ozenda, André M. Sonnet, Epifanio G. Virga

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
15 Downloads (Pure)


Nematic polymer networks are (heat and light) activable materials, which combine the features of rubber and nematic liquid crystals. When only the stretching energy of a thin sheet of nematic polymer network is minimized, the intrinsic (Gaussian) curvature of the shape it takes upon (thermal or optical) actuation is determined. This, unfortunately, produces a multitude of possible shapes, for which we need a selection criterion, which may only be provided by a correcting bending energy depending on the extrinsic curvatures of the deformed shape. The literature has so far offered approximate corrections depending on the mean curvature. In this paper, we derive the appropriate bending energy for a sheet of nematic polymer network from the celebrated neo-classical energy of nematic elastomers in three space dimensions. This task is performedviaa dimension reduction based on a modified Kirchhoff-Love hypothesis, which withstands the criticism of more sophisticated analytical tools. The result is a surface elastic free-energy density where stretching and bending are blended together; they may or may not be length-separated, and should be minimized together. The extrinsic curvatures of the deformed shape not only feature in the bending energy through the mean curvature, but also through the relative orientation of the nematic director in the frame of the directions of principal curvatures.

Original languageEnglish
Pages (from-to)8877-8892
Number of pages16
JournalSoft Matter
Issue number38
Early online date4 Aug 2020
Publication statusPublished - 14 Oct 2020


  • cond-mat.soft
  • math-ph
  • math.MP
  • nematic polymer networks
  • modified Kirchhoff-Love hypothesis


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