Folding, crumpling and entangling of sheets and filaments

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Nontechnical Abstract:The goal of the project is to study large shape transformations of thin sheets and filaments when twisted while being held under tension, using noninvasive 3D laser and x-ray scanning techniques. The study will relate the evolution of the structure to its strength in terms of its torsional response far above the onset of initial buckling and after they come in self-contact. The study will focus on complementary hyperelastic materials which can stretch significantly compared to their size, and inextensible materials which bend and deform plastically. The element-level measurements of the internal structure will be analyzed in terms of physical models which incorporate their geometry and elasticity response. Fundamental understanding of the shape and strength of elastomers under large deformations will impact the development of a wide range of materials, including functional yarns and synthetic tissues. The results will be published in peer reviewed journals and will increase scientific knowledge in the field of condensed matter physics and will be disseminated freely via the internet. The project work will support undergraduate student internships and the research work of graduate students towards their dissertations. The research and mentoring activity will result in educating undergraduate and graduate students pursuing careers in STEM related disciplines, and outreach activities to K-12 students. Technical Abstract:The goal of the project is to study topological transformations of thin sheets and filaments as they are driven to collapse and self-packing under extreme boundary loading. The geometry as a function of applied boundary loading will be obtained using noninvasive 3D laser and x-ray scanning techniques and characterizing the surface curvatures and energetics. The study will focus on complementary reversible and irreversible strain-transformed materials in the nonperturbative deformation regime beyond the reach of classical elasticity theories. A filament model based on the origami kinematics will be developed to explain the emergence of self-folds, twist localization and helical wrapping. Damage networks will be analyzed with random and spatially correlated fold algorithms to identify the processes that shape sheet singularities, and their compliance under repeated quenching using torque measurements. The relative contribution of the elasticity of the elements and the contact mechanics will be probed to understand the shaping of yarns and tissues. The results will be published in peer reviewed journals and will increase scientific knowledge in the field of condensed matter physics, biomaterials, and rapid prototyping. The research and mentoring activity will result in educating multi-generational groups of students pursuing careers in STEM related disciplines. The project work will support undergraduate student internships and the research work of graduate students towards their dissertations.This DMR grant supports research on topological transformation of sheets and filaments under extreme stress with funding from the Condensed Matter Physics (CMP) Program in the Division of Materials Research of the Mathematical and Physical Sciences Directorate.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.