Instabilities, asymptotic isometry, and energy condensation in elastic sheets under twist

该项目的目标是深入了解薄弹性材料在受到扭曲时如何发生屈曲和折痕。这方面的知识对于从石墨烯片、纳米管、半导体纳米带和各种生物材料等新材料制成的设备中获得最大功能至关重要。 对薄板在应力作用下如何屈曲和起皱的理论认识还处于起步阶段，这些实验研究将为这些理论提供指导和检验。 最终，这项研究将影响薄材料在应力下的强度和失效的确定，以及通过开发可广泛扩展的技术来图案化细长材料来制造柔性结构和纱线。 拟议的研究也将对教育学生追求STEM相关学科的职业产生重大影响。研究生的论文研究工作将受到资助的影响。该项目将提高本科生在实验室的研究经验。技术段落该项目的目标是了解薄弹性板的屈曲不稳定性受到扭曲，导致扭曲，应力集中和能量凝聚到折痕结构。弹性和几何形状的基本作用，在组织后屈曲结构的形状将与实验，将测量的结构，使用微X射线断层扫描技术和激光辅助光学成像技术的形状进行调查。由一个新开发的协变形式的Foppl-von Karman方程的薄板所预期的相图将被调查的功能板的纵横比和弹性模量。 发展过程中观察到的薄带状扭曲的最小的脊结构和它们的相互作用将被用来研究作为板厚度和施加变形的函数的相关能量的缩放。了解自卷曲纱线和织物结构在扭曲下的形成将提供一种替代的可靠和有效的策略，以利用包括石墨烯片、纳米管、半导体纳米带和生物材料在内的新型材料来构建介观层次结构。同行评审的科学出版物将增加凝聚态物理学领域的科学知识，并将在网上传播。本科生和研究生将接受弹性和软物质领域的培训，并使用先进的成像技术和分析来从事STEM职业。

Nontechnical AbstractThe goal of the project is to develop a deep understanding of how thin elastic materials undergo buckling and creasing when subjected to twist. This knowledge is essential in obtaining the maximum functionality from devices made with new materials such as graphene sheets, nanotubes, semiconductor nanoribbons, and various biomaterials. Theoretical understanding of how thin sheets buckle and crease under stress is just in its infancy and these experimental studies will provide both guidance to and tests of these theories. Ultimately, this research will impact determination of strength and failure of thin materials under stress, and manufacturing of flexible structures and yarns by developing widely scalable techniques to pattern slender materials. The proposed research will also have a significant impact on educating students pursuing careers in STEM related disciplines. The dissertation research work of graduate students will be impacted by the grant. The project will enhance research experience of undergraduate students in the laboratory.Technical ParagraphThe goal of the project is to understand the buckling instabilities of thin elastic sheets subjected to twist which lead to wrinkling, stress focusing and energy condensation into creased structures. The fundamental role of elasticity and geometry in organizing the shape of the post-buckled structures will be investigated with experiments which will measure the shapes of the structures using micro x-ray tomography techniques and laser-aided optical imaging techniques. The phase diagram anticipated by a newly developed co-variant form of the Foppl-von Karman equations for thin plates will be investigated as function of sheet aspect ratio and elastic modulus. Development of minimal ridge structures and their interactions observed during the twisting of thin ribbon shapes will be used to study the scaling of the associated energy as a function of sheet thickness and applied deformation. Understanding formation of self-scrolled yarn and fabric structures under twist will provide an alternate reliable and efficient strategy to build mesoscale hierarchical structures with novel materials including graphene sheets, nanotubes, semiconductor nanoribbons, and biomaterials. Peer reviewed scientific publications will increase scientific knowledge in the field of condensed matter physics and will be disseminated on the web. Undergraduate and graduate students will be trained in the field of elasticity and soft matter, and in using sophisticated imaging techniques and analysis towards careers in STEM.