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打印对于原型制作来说已经足够便宜，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，有许多材料可以被制成从平板可控地生长成目标三维结构。PI的团队将开发理解和设计工具，以最佳方式将薄片折叠并弯曲成目标形状，并研究弹性片材如何起皱以适应曲率。这些项目共同揭示了弹性和几何形状之间的关系，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，使其能够在先进制造和软机器人中应用。该奖项有助于研究生和本科生在多学科领域的教育，并通过与实验研究小组的大量互动。它也支持PI的努力，在推广到一般公众。技术摘要该奖项支持的三维结构形成的二维弹性片的研究。聚合物结构制造的最新进展已经允许开发活性材料，其可以通过空间非均匀生长而弯曲成目标三维结构。这个研究项目有两个目标。首先，它将扩展的数学基础奠定了理解屈曲的薄膜，由于不均匀的增长，使设计的最佳模式的增长。第二，探讨薄板如何借由弯曲而符合曲面的相关问题。第二个项目的结果将用于探索当一个不断增长的薄板不能通过平滑屈曲来缓解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，使其能够在先进制造和软机器人中应用。该奖项有助于研究生和本科生在多学科领域的教育，并通过大量的实验互动。它还支持PI努力与公众联系。

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.