scholarly journals A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation

2017 ◽  
Vol 55 (3) ◽  
pp. 1357-1386 ◽  
Author(s):  
Ricardo H. Nochetto ◽  
Shawn W. Walker ◽  
Wujun Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Variable Degree ◽  
Degree Of Orientation ◽  
Element Method

A finite element method for the generalized Ericksen model of nematic liquid crystals

2020 ◽  
Vol 54 (4) ◽  
pp. 1181-1220 ◽  
Author(s):  
Shawn W. Walker
Keyword(s):  
Finite Element ◽  
Liquid Crystals ◽  
Elastic Constants ◽  
Variable Degree ◽  
Element Discretization ◽  
Continuous Energy ◽  
Degenerate Elliptic ◽  
Degree Of Orientation ◽  
Electric Effects ◽  
Fully Coupled

We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent “elastic”constants that depends on two order parameters n (director) and s (variable degree of orientation). In addition, we present a new finite element discretization for this energy, that can handle the degenerate elliptic part without regularization, with the following properties: it is stable and it Γ-converges to the continuous energy. Moreover, it does not require the mesh to be weakly acute (which was an important assumption in our previous work). Furthermore, we include other effects such as weak anchoring (normal and tangential), as well as fully coupled electro-statics with flexo-electric and order-electric effects. We also present several simulations (in 2-D and 3-D) illustrating the effects of the different elastic constants and electric field parameters.

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