单轴拉伸弹性薄膜中平面区与褶皱区的转变
Transition between planar and wrinkled regions in uniaxially stretched thin elastic film
摘要：
研究了单轴拉伸弹性薄膜从平坦区到褶皱区的转变。我们建立了一个模型变分问题，并研究了它的基态能量。使用已知的缩放边界的最小能量，最小能量可以写为最小的基本（凸）松弛问题加上一个项，它在膜的厚度线性增长。我们表明，在消失厚度的限制，前因子的标度律的原问题可以通过最小化简单的标量约束变分问题。
英文摘要：
We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal energy can be written as a minimum of the underlying (convex) relaxed problem plus a term, which grows linearly in the thickness of the film. We show that in the limit of vanishing thickness the prefactor in the scaling law for the original problem can be obtained by minimization of simpler scalar constrained variational problems.
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