Metric-induced buckling and buckling-induced metrics

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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.