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

薄材料可以弯曲、扭曲和起皱成多种形状。由此产生的形状可以是平滑的，就像花朵起伏的边缘，也可以是尖锐的，就像皱巴巴的锡箔球上的折痕和点。这项研究的目的是了解这些特征何时变得平滑，何时变得尖锐。这个看似简单的问题却出人意料地难以回答，它影响了依赖于薄片的各种技术。该项目包括一套模型实验，其中聚合物薄膜被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标度的物理行为，因此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联项目相结合。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中央纽约，谁将进行为期6周的夏季研究实习高中教师。技术摘要尽管在我们的日常生活中无处不在的床单和它们的重要性，一系列的技术，我们仍然缺乏一个一般的预测框架，当一个弯曲的床单将有一个光滑或尖锐的字符。该项目的首要目标是测量，量化和预测弹性膜何时会形成尖锐的奇异特征，其中应力和应变自发地凝聚到一个小集合。该项目的重点是没有施加拉伸载荷来组织屈曲模式的情况。一组实验将使用冲压装置，其中薄片被限制在两个弯曲壁之间的差距中。第二组实验将研究限制在液体浴中的球形帽的屈曲。屈曲模式的范围从光滑的同心圆皱纹，近晶域的平行皱纹分离尖锐的晶界。该项目将描述这些形态之间的过渡，同时追求一个诱人的链接到锯齿状外壳的金属化过渡。该研究处于物理学、应用数学和工程学的交叉点，该项目涉及凝聚态物质的一般主题，包括奇点、对称性破缺和有序-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价值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.