Corner singularities and shape of stretched elastic sheets
Corner singularities and shape of stretched elastic sheets
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DOI：
10.1103/physreve.98.043003
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发表时间：
2018-10-17
影响因子：
2.4
通讯作者：
Kudrolli, Arshad
中科院分区：
文献类型：
--
作者：
Chopin, Julien;Panaitescu, Andreea;Kudrolli, Arshad
本文通过实验、数值分析和双调和弹性方程的渐近分析，研究了纵向拉伸矩形薄板在两个相对边界处固定和自由的变形。通过跟踪嵌入的荧光示踪剂与数字图像相关技术测量片材的位移场。实验和数值有限元分析被认为是在整体良好的协议，除了在非常角落，发生大变形。我们发现，变形板可以大致分为一个单轴拉伸的中心区域和两个夹紧为主的侧部区域。一个子区域，其特征在于分散的应力可以确定在四个钳位的自由角的钳位主导的区域内的每个。我们假设，在角落处的分歧是正规化的非线性弹性变形发生在这个子区域中的非常角落，并提供了一个非平凡的缩放其大小。在中间角点占主导的子区域内，测得的位移随着与角点的距离r而增长，即r（α），幂α < 1，这与自由边和固定边相交处的应力奇异性的发展一致。
We investigate the deformation of a longitudinally stretched rectangular sheet which is clamped at two opposite boundaries and free otherwise with experiments, numerical analysis, and asymptotic analysis of the biharmonic elastic equation governing their planar equilibrium configurations. The displacement field of the sheet is measured by tracking embedded fluorescent tracers with a digital image correlation technique. The experiments and numerical finite-element analysis are found to be in overall good agreement except at the very corners where large deformations occur. We find that the deformed sheet can be broadly divided into a uniaxially stretched central region and two clamp-dominated side regions. A subregion characterized by a diverging stress can be identified at each of the four clamped-free corners within the clamp-dominated region. We postulate that the divergence at the corners is regularized by nonlinear elastic deformations occurring in this subregion at the very corners and provide a nontrivial scaling for its size. Within the intermediate corner-dominated subregion, measured displacements grow with distance r from the corners as r(alpha), with power alpha < 1 consistent with the development of stress singularities at the intersection of the free and clamped edges.