Variational modelling of nematic elastomer foundations

Pierluigi Cesana, Andrés A.León Baldelli

研究成果: Contribution to journalArticle査読

抄録

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.

本文言語英語
ページ(範囲)2833-2861
ページ数29
ジャーナルMathematical Models and Methods in Applied Sciences
28
14
DOI
出版ステータス出版済み - 12 30 2018

All Science Journal Classification (ASJC) codes

  • モデリングとシミュレーション
  • 応用数学

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