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How far does a fold go?
Extreme Mechanics Letters ( IF 4.7 ) Pub Date : 2021-03-08 , DOI: 10.1016/j.eml.2021.101261
Atul Bhaskar , Kevin Jose

We assess the spatial spread of a fold within a narrow elastic strip theoretically and computationally in the small deflection regime. We consider a hierarchy of folding-response ansatz, suitable for stretch-free deformation. The role of Poisson’s coupling between the two curvatures, and that of surface twist, is brought out. Here we show that there exists a critical Poisson’s ratio separating the regime of monotonically decaying fold profiles from that of decaying oscillatory folds. A spatially separable solution results in length-wise localised folds, the length scale of which is in excellent agreement with that obtained from simulations. The persistence length shows significant sensitivity to the Poisson’s ratio of the material. We also establish a mathematical analogy of the folding problem, with one of elastic structures on foundations, the restoring force being proportional to local deflection as well as shear in the foundation.



中文翻译:

褶皱能走多远?

我们在理论上和计算上在小挠度范围内评估狭窄弹性带内褶皱的空间扩展。我们考虑了适合无拉伸变形的折叠响应ansatz的层次结构。提出了两个曲率之间的泊松耦合作用以及表面扭曲的作用。在这里,我们表明存在一个临界的泊松比,它将单调衰减折叠轮廓的形式与衰减振荡折叠的形式分开。在空间上可分离的解决方案会导致纵向局部折叠,其长度比例与从模拟获得的比例非常吻合。持久长度显示出对材料的泊松比的显着敏感性。我们还建立了折叠问题的数学类比,其中一个弹性结构位于地基上,

更新日期:2021-03-22
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