Nematic elastomers: Gamma-limits for large bodies and small particles

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Abstract

We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank theory), we prove that we obtain a fully biaxial nematic texture (that of the de Gennes theory) as a by-product of the relaxation phenomenon connected to Gamma-convergence. In the case of small particles, we show that formation of new microstructure is not possible, and we describe the map of minimizers of the Gamma-limit as the phase diagram of the mechanical model.

Original languageEnglish
Pages (from-to)2354-2383
Number of pages30
JournalSIAM Journal on Mathematical Analysis
Volume43
Issue number5
DOIs
Publication statusPublished - Nov 21 2011
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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