scholarly journals Exchange-energy functionals for finite two-dimensional systems

2007 ◽  
Vol 76 (23) ◽  
Author(s):  
S. Pittalis ◽  
E. Räsänen ◽  
N. Helbig ◽  
E. K. U. Gross
Keyword(s):  
Exchange Energy ◽  
Two Dimensional ◽  
Energy Functionals

A reexamination of exchange energy functionals

1999 ◽  
Vol 111 (13) ◽  
pp. 5656-5667 ◽  
Author(s):  
Takao Tsuneda ◽  
Toshihisa Suzumura ◽  
Kimihiko Hirao
Keyword(s):  
Exchange Energy ◽  
Energy Functionals

scholarly journals Variational modelling of nematic elastomer foundations

2018 ◽  
Vol 28 (14) ◽  
pp. 2863-2904
Author(s):  
Pierluigi Cesana ◽  
Andrés A. León Baldelli
Keyword(s):  
Liquid Crystal ◽  
Integral Functional ◽  
Elastic Membrane ◽  
Two Dimensional ◽  
Order Tensor ◽  
Asymptotic Regime ◽  
Liquid Crystal Elastomer ◽  
Energy Functionals ◽  
Shear Energy ◽  
Dimensional Integral

We compute the [Formula: see text]-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.

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