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Coil–stretch-like transition of elastic sheets in extensional flows
Soft Matter ( IF 3.4 ) Pub Date : 2020-11-04 , DOI: 10.1039/d0sm01630f
Yijiang Yu 1, 2, 3, 4 , Michael D. Graham 1, 2, 3, 4
Affiliation  

The conformation of a long linear polymer dissolved in fluid and exposed to an extensional flow is well-known to exhibit a “coil–stretch” transition, which for sufficiently long chains can lead to bistability. The present work reports computations indicating that an analogous “compact–stretched” transition arises in the dynamics of a thin elastic sheet. Sheets of nominally circular, square or rectangular shape are simulated in planar and biaxial flows using a finite element method for the sheet conformations and a regularized Stokeslet method for the fluid flow. If a neo-Hookean constitutive model is used for the sheet elasticity, the sheets will stretch without bound once a critical extension rate, as characterized nondimensionally by a capillary number, is exceeded. Nonlinear elasticity, represented with the Yeoh model, arrests the stretching, leading to a highly-stretched steady state once the critical capillary number is exceeded. For all shapes and in both planar and biaxial extension, a parameter regime exists in which both weakly stretched (compact) and strongly stretched states can be found, depending on initial conditions. I.e. this parameter regime displays bistability. As in the long-chain polymer case, the bistable behavior arises from the hydrodynamic interaction between distant elements of the sheet, and vanishes if these interactions are artificially screened by use of a Brinkman model for the fluid motion. While the sheets can transiently display wrinkled shapes, all final shapes in planar and biaxial extension are planar.

中文翻译:

拉伸流中弹性片的线圈状拉伸状转变

众所周知,溶解在流体中并暴露于延伸流中的长线性聚合物的构象会表现出“线圈-拉伸”过渡,这对于足够长的链会导致双稳性。本工作报告了计算结果,表明在薄弹性片的动力学中出现了类似的“紧缩拉伸”转变。使用平面有限元方法和平面流的Stokeslet方法在平面和双轴流中模拟名义上为圆形,正方形或矩形的薄片。如果将新霍克本构模型用于片材弹性,则一旦超过临界伸长率(由毛细管数无量纲地表征),则片材将不受约束地拉伸。用Yeoh模型表示的非线性弹性阻止了拉伸,一旦超过临界毛细管数,将导致高度拉伸的稳态。对于所有形状,在平面和双轴延伸中,都存在一个参数范围,其中取决于初始条件,可以找到弱拉伸(压缩)状态和强拉伸状态。即,该参数方案显示双稳态。如在长链聚合物的情况下一样,双稳态行为是由片材的远距离元素之间的流体动力相互作用引起的,如果通过使用Brinkman模型对流体运动进行人工筛选,则这些相互作用将消失。尽管片材可以暂时显示起皱的形状,但所有在平面和双轴延伸方向上的最终形状都是平面的。
更新日期:2020-11-12
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