Numerical Study of Liquid Crystal Elastomer Using Mixed Finite Element Method. (arXiv:0911.5415v1 [math.NA])

In this paper, we tried to model the elastic behavior of liquid crystal
elastomer using mixed finite element method. We start from an energy functional
which includes Blandon's stored energy of LCE, penalization of change of
directors, and two Lagrangian terms enforcing incompressibility and the unity
of the directors. The resulting Euler-Lagrange equation is a nonlinear equation
of the displacement ${mathbf u}$, the director ${mathbf n}$, the pressure $p$
and the Lagrange multiplier $lambda$. Inf-sup conditions for the
well-posedness of the linearized system were proposed and some are proved. For
those inf-sup conditions that are not easy to prove, we suggest ways to do the
numerical verification (the inf-sup tests). Finally, some numerical results are
presented.

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Original source : http://arxiv.org/abs/0911.5415...