论文标题
列Nematic LCE杆的建模和仿真
Modeling and simulation of nematic LCE rods
论文作者
论文摘要
我们引入了一个由列液液晶体弹性体组成的不可延迟的Bi-Rod的非线性，一维弯曲模型。该模型结合了曲率二次和扭转的弹性能，以及用于液晶弹性体的Frank-Oseen能量。此外，该模型具有列合弹性耦合，该耦合将晶体方向与自发弯曲扭动术语相关联。我们表明该模型可以从三维非线性弹性中得出$γ$限制。此外，我们引入了一种数值方案，以通过离散的梯度流量计算弯曲模型的临界点。我们提出了各种数值模拟，这些模拟说明了该模型预测的丰富机械行为。数值实验揭示了该方法的良好稳定性和近似特性。
We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a Frank-Oseen energy for the liquid crystal elastomer. Moreover, the model features a nematic-elastic coupling that relates the crystalline orientation with a spontaneous bending-twisting term. We show that the model can be derived as a $Γ$-limit from three-dimensional nonlinear elasticity. Moreover, we introduce a numerical scheme to compute critical points of the bending-twisting model via a discrete gradient flow. We present various numerical simulations that illustrate the rich mechanical behavior predicted by the model. The numerical experiments reveal good stability and approximation properties of the method.
