论文标题
液晶聚合物网络的减少膜模型：渐近和计算
Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation
论文作者
论文摘要
我们通过渐近和计算检查了液晶聚合物网络（LCN）的膜模型的减少。该模型需要解决非凸拉伸能量的最小化问题。我们显示了来自3D橡胶弹性的2D膜模型的形式渐近推导。我们构建具有点缺陷的近似解决方案。我们设计了一种有限的元素方法，并提出了具有牛顿内部迭代的非线性梯度流，以解决非convex离散最小化问题。我们介绍了实际利益的数值模拟，以说明模型的能力和我们捕获丰富的物理现象的方法。
We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of the 2D membrane model from 3D rubber elasticity. We construct approximate solutions with point defects. We design a finite element method with regularization, and propose a nonlinear gradient flow with Newton inner iteration to solve the non-convex discrete minimization problem. We present numerical simulations of practical interests to illustrate the ability of the model and our method to capture rich physical phenomena.
