Metric-induced buckling and buckling-induced metrics

该奖项支持物理学、材料科学和工程学之间的理论研究和教育。虽然3D打印已经变得足够便宜，可以制作原型，但作为一种制造技术，它有许多缺点，包括速度和可配置性。然而，有许多材料可以被控制地从平板生长到目标三维结构。PI的团队将开发理解和设计工具，以优化薄片的折叠和扣入目标形状，并研究弹性薄片如何皱褶以适应曲率。总之，这些项目揭示了弹性和几何之间的关系，并使工具的开发能够改善结构材料的制造。这项工作将通过引入新的分析技术来预测三维结构，从而对结构材料的设计产生影响，从而使先进制造和软机器人技术得以应用。该奖项通过与实验研究小组的大量互动，在多学科领域为研究生和本科生的教育做出了贡献。它还支持PI向公众宣传的努力。该奖项支持二维弹性薄片中三维结构形成的研究。聚合物结构制造的最新进展使活性材料的发展成为可能，这些活性材料可以通过空间非均匀生长，弯曲成目标三维结构。这个研究项目有两个目标。首先，它将扩展所奠定的数学基础，以理解由于不均匀生长而导致的薄膜屈曲，从而允许设计最佳的生长模式。其次，它将探讨一个相关的问题，如何一个板可以符合弯曲的表面起皱。第二个项目的结果将用于探索当生长的薄片不能通过平滑屈曲来减轻其所有面内应力时会发生什么。这项工作将通过引入新的分析技术来预测三维结构，从而对结构材料的设计产生影响，从而使先进制造和软机器人技术得以应用。该奖项通过与实验的大量互动，在多学科领域为研究生和本科生的教育做出了贡献。它还支持PI向公众宣传的努力。

Nontechnical SummaryThis award supports theoretical research and education at the interface between physics, materials science and engineering. Though 3D printing has become inexpensive enough for prototyping, it has numerous drawbacks as a manufacturing technique, including speed and configurability. Yet, there are a number of materials that can be made to controllably grow from a flat sheet to a targeted three-dimensional structure. The PI's group will develop understanding and design tools to optimally pattern a thin sheet to fold and buckle into a targeted shape and study how an elastic sheet wrinkles to accommodate curvature. Together, these projects unveil the relationship between elasticity and geometry, and enable the development of tools to improve manufacturing of structured materials.The work will have an impact on the design of structured materials by introducing new analytical techniques for the prediction of three-dimensional structures, enabling applications in advanced manufacturing and soft robotics. The award contributes to the education of graduate and undergraduate students in a multidisciplinary field and through substantial interactions with experimental research groups. It also supports the PI's efforts at outreach to the general public.Technical SummaryThis award supports studies of three-dimensional structure formation in two-dimensional elastic sheets. Recent progress in the fabrication of polymeric structures have allowed the development of active materials that can, through spatially non-uniform growth, buckle into targeted three-dimensional structures. This research project has two goals. First, it will extend the mathematical foundation laid down to understand the buckling of thin films due to non-uniform growth to allow the design of optimal pattern of growth. Second, it will explore the related problem of how a sheet can conform to a curved surface by wrinkling. The results of this second project will then be used to explore what happens when a growing sheet cannot alleviate all of its in-plane stresses by buckling smoothly.The work will have an impact on the design of structured materials by introducing new analytical techniques for the prediction of three-dimensional structures, enabling applications in advanced manufacturing and soft robotics. The award contributes to the education of graduate and undergraduate students in a multidisciplinary field and through substantial interactions with experiments. It also supports the PI's efforts at outreach to the general public.