Crumple Dynamics and Interactions Mediating Elastic Deformations of Structures

薄板壳结构从细胞膜到衣物到飞机壁板再到储罐，在许多长度尺度上的弹性变形都具有局部化的拉伸和弯曲特征。这通常被简单地称为“皱缩”，而大变形的小区域则是“皱缩”。人们观察到，褶皱在实现薄结构的大规模变形方面发挥了重要作用，通常是通过目前尚未得到很好记录或了解的快速瞬时动态行为。这一奖项将通过一个简单的模型系统和两种不同的理论方法来促进对这些基本变形过程的研究。这项工作将有助于通过开发降阶模型来对多尺度弹性系统中的复杂现象进行建模和控制，这些现象非常复杂，难以实时模拟，例如航空航天应用中的气动热弹性现象。结果也将适用于结构力学、柔顺机构、软机器人和一些生物系统的其他分支。该奖项将支持一名博士后研究员，并培训一批高级结构力学的研究生和本科生，后者涉及与合作者的国际交流。PI和学生们还将共同开发一个针对当地初中和高中年轻女性的暑期科学和工程项目的教育模块。该奖项的目标是量化和模拟变形板块中局部弹性区域(褶皱)的细观力学，重点关注这些局部褶皱在通过准静态和快速瞬时动力学调节全球变形中所起的作用。这项工作建立在初步实验的基础上，展示了有序图案序列、单个皱折的成核以及皱缩-皱缩或皱缩-边界相互作用等现象。本文将采用两种理论方法。人们将利用来自结构力学和图案形成系统的想法，在这些系统中，在连续统中的局部图案之间发生“蜿蜒”的转变。另一种是将褶皱的新粒子级描述作为单独的离散实体，这些实体可以与背景曲率场、彼此之间以及与边界交互。这些方法将伴随着对弯曲薄板上的力和曲率的定量实验测量。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The elastic deformation of thin plate and shell structures at many length scales, from cell membranes to clothing to aircraft panels to storage tanks, is characterized by the localization of stretching and bending. This is often simply called “crumpling”, and the small regions of large deformations “crumples”. Crumples are observed to play an important role in enabling the large-scale deformations of thin structures, often through rapid transient dynamic behavior that is currently not well documented or understood. This award will facilitate the study of these fundamental deformation processes through experiments on a simple model system and two different theoretical approaches. Insights from this work will aid in the modeling and control of complex phenomena in multi-scale elastic systems that are prohibitively complex to simulate in real time through the development of reduced-order models, e.g., the aero-thermo-elastic phenomena in aerospace applications. Results will also be applicable to other branches of structural mechanics, compliant mechanisms, soft robotics, and some biological systems. The award will support a postdoctoral researcher and train a group of graduate and undergraduate students in advanced structural mechanics, with the latter involving international exchanges with collaborators. The PI and students will also co-develop an education module for a summer science and engineering program for young women in local middle and high schools.The objective of this award is to quantify and model the meso-scale mechanics of localized elastic regions (crumples) in deforming plates, focusing on the role these localized crumples play in mediating global deformations through both quasistatic and rapid transient dynamics. The work builds on preliminary experiments demonstrating phenomena such as sequences of ordered patterns, nucleation of individual crumples, and crumple-crumple or crumple-boundary interactions. Two theoretical approaches will be employed. One will leverage ideas from structural mechanics and pattern-forming systems, where “snaking” transitions occur between localized patterns in continua. Another will take a novel particle-level description of crumples as individual discrete entities that can interact with a background curvature field, with each other, and with boundaries. These approaches will be accompanied by quantitative experimental measurements of forces on, and curvatures of, buckled sheets.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.