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

点击翻译按钮获取中文摘要

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.