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。这些知识对于从新材料（如石墨烯片、纳米管、半导体纳米带和各种生物材料）制成的设备中获得最大功能至关重要。关于薄板在压力下如何弯曲和折痕的理论理解还处于起步阶段，这些实验研究将为这些理论提供指导和测试。最终，这项研究将影响薄材料在应力下的强度和破坏的确定，以及通过开发广泛可扩展的技术来制造柔性结构和纱线。拟议的研究也将对教育追求STEM相关学科职业的学生产生重大影响。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。该项目的目标是了解薄弹性板在扭曲作用下的屈曲不稳定性，这种不稳定性会导致起皱、应力集中和能量凝聚成折痕结构。弹性和几何在组织后屈曲结构形状中的基本作用将通过实验进行研究，实验将使用微x射线断层扫描技术和激光辅助光学成像技术测量结构的形状。本文将研究新开发的Foppl-von Karman方程的共变形式所预测的相图作为薄片长径比和弹性模量的函数。最小脊结构的发展及其在薄带状扭曲过程中观察到的相互作用将用于研究相关能量作为薄片厚度和施加变形的函数的缩放。了解自卷曲纱线和织物结构在捻度下的形成，将为用石墨烯片、纳米管、半导体纳米带和生物材料等新型材料构建中尺度分层结构提供可靠而有效的替代策略。同行评议的科学出版物将增加凝聚态物理领域的科学知识，并将在网络上传播。本科生和研究生将接受弹性和软物质领域的培训，并在STEM职业中使用复杂的成像技术和分析。

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.