Paulsen Joseph D, Démery Vincent, Toga K Buğra, Qiu Zhanlong, Russell Thomas P, Davidovitch Benny, Menon Narayanan
Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France.
Phys Rev Lett. 2017 Jan 27;118(4):048004. doi: 10.1103/PhysRevLett.118.048004.
Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.
由于存在自接触、几何非线性以及众多低能态等复杂因素，预测薄弹性片材的大幅度变形颇具难度。我们研究了一种简单的二维情形，即漂浮在空气 - 水界面上的环形聚合物片材，其内外边缘受到不同的张力。该片材会折叠并形成许多打破轴对称性的独特形态。这些状态可以通过一种近期的几何方法来理解，该方法通过使一个合适的面积泛函取极值来确定极度可弯曲但不可拉伸片材的总体形状。我们的分析解释了一个显著特征，即观察到的褶皱形状和折叠形状之间的屈曲转变对片材的弯曲刚度不敏感。
