A relaxed model and its homogenization for nematic liquid crystals in composite materials

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Abstract

We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen-Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non-linear. We employ two-scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models.

Original languageEnglish (US)
Pages (from-to)1125-1143
Number of pages19
JournalMathematical Methods in the Applied Sciences
Volume27
Issue number10
DOIs
StatePublished - Jul 10 2004

Keywords

  • Composite materials
  • Energy minimization
  • Homogenization
  • Liquid crystals

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