Variational modelling of nematic elastomer foundations

Pierluigi Cesana, Andrés A.León Baldelli

Research output: Contribution to journalArticle

Abstract

We compute the σ-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the vanishing thickness of the membranes and the ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film.

Original languageEnglish
Pages (from-to)2833-2861
Number of pages29
JournalMathematical Models and Methods in Applied Sciences
Volume28
Issue number14
DOIs
Publication statusPublished - Dec 30 2018

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All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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