Zhu Wei, Shelley Michael, Palffy-Muhoray Peter
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051703. doi: 10.1103/PhysRevE.83.051703. Epub 2011 May 12.
We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation are used, within a Lagrangian framework, to obtain the equations of motion. The free energy consists of both elastic and liquid crystalline contributions, each of which is a function of the material displacement and the orientational order parameter. The model gives dynamics for the material displacement, the scalar order parameter and the nematic director, the latter two of which correspond to the orientational order parameter tensor. Our simulations are carried out by solving the governing equations using an implicit-explicit scheme and the Chebyshev polynomial method. The simulations show that the model can successfully capture the shape changing dynamics of LCEs that have been observed in experiments, and also track the evolution of the order parameter tensor.
我们考虑一个描述向列型液晶弹性体（LCEs）动态行为的连续介质模型，并实施一种数值方案来求解控制方程。在该模型中，在拉格朗日框架内使用亥姆霍兹自由能和瑞利耗散来获得运动方程。自由能由弹性贡献和液晶贡献组成，每一项都是材料位移和取向序参量的函数。该模型给出了材料位移、标量序参量和向列型指向矢的动力学，后两者对应于取向序参量张量。我们的模拟通过使用隐式 - 显式格式和切比雪夫多项式方法求解控制方程来进行。模拟结果表明，该模型能够成功捕捉实验中观察到的LCEs的形状变化动力学，并且还能追踪序参量张量的演化。
