Understanding stress focusing in thin solids in the absence of tensile loads

非技术摘要薄材料可以弯曲、扭曲和起皱成多种形式。产生的形状可以像花朵起伏的边缘一样平滑，也可以像皱巴巴的锡箔球中的折痕和尖端一样尖锐。这项研究的目的是了解这些特征什么时候变得光滑，什么时候变得尖锐。这个看似简单的问题令人惊讶地难以回答，它影响了各种依赖薄板的技术。该项目由一套模型实验组成，在这些实验中，聚合物薄膜被强迫进入不同的几何形状，迫使它们弯曲。由于该项目关注的是应该是无尺度的物理行为，我们的发现应该适用于从非常小到非常大的材料系统，从石墨烯薄膜到食品包装再到可部署的卫星。这项研究与一系列针对广泛受众的教育和外展项目相结合。该项目将培养两名博士生，他们将在实验室与本科生和高中生一起工作。这项工作还将聘请来自纽约市中心的高中教师，他们将进行为期6周的暑期研究实习。技术摘要尽管薄片在我们的日常生活中无处不在，它们对一系列技术的重要性，但我们仍然缺乏一个通用的预测框架来预测何时弯曲的薄片将具有光滑或尖锐的特征。该项目的首要目标是测量、量化和预测弹性薄膜何时会形成尖锐的、奇异的特征，在这些特征中，应力和应变自发地浓缩到一个小集合中。该项目侧重于没有施加拉伸载荷来组织屈曲模式的情况。其中一组实验将使用冲压装置，其中薄片被限制在两个弯曲的墙之间的缝隙中。第二组实验将研究限制在液浴中的超薄球帽的屈曲。屈曲模式从光滑的同心圆形皱纹，到由尖锐的晶界分隔的平行皱纹的近晶区。该项目将描述这些形态之间的转变，同时追求一个诱人的链接，以在凹陷的贝壳中实现多角化转变。这项研究涉及物理学、应用数学和工程学，该项目涉及凝聚态物质的一般主题，包括奇点、对称破缺和有序-无序转变。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。

Nontechnical AbstractThin materials can be bent, twisted, and wrinkled into a multitude of forms. The resulting shapes can be smooth like the undulating edge of a flower, or sharp like the creases and points in a crumpled ball of foil. The goal of this research is to understand when these features turn out to be smooth versus when they are sharp. This deceptively simple question is surprisingly difficult to answer, and it impacts a variety of technologies that rely on thin sheets. This project consists of a suite of model experiments where polymer films are forced into different geometries, forcing them to buckle. Because the project focuses on physical behaviors that should be scale-free, our discoveries should be applicable to material systems ranging from the very small to the very large, from graphene films to food packaging to deployable satellites. The research is coupled to a set of education and outreach projects that target a wide range of audiences. The project will train two PhD students who will work with undergraduates and high school students in the lab. The work will also engage high school teachers from Central New York, who will conduct 6-week summer research internships. Technical AbstractDespite the ubiquity of sheets in our everyday lives and their importance to a range of technologies, we nevertheless lack a general predictive framework for when a buckled sheet will have a smooth or sharp character. The overarching goal of the project is to measure, quantify, and predict when an elastic film will form sharp, singular features where stresses and strains spontaneously condense to a small set. The project focuses on situations where there are no applied tensile loads to organize the buckling patterns. One set of experiments will use a stamping setup where a thin sheet is confined in the gap between two curved walls. A second set of experiments will investigate the buckling of an ultrathin spherical cap confined to a liquid bath. The buckling patterns range from smooth concentric circular wrinkles, to smectic domains of parallel wrinkles separated by sharp grain boundaries. The project will characterize the transitions between these morphologies while pursuing a tantalizing link to a polygonalization transition in indented shells. This research lies at the intersections of physics, applied mathematics, and engineering, and the project engages with general themes in condensed matter including singularities, symmetry breaking, and order-disorder transitions.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.