Folding, crumpling and entangling of sheets and filaments

非技术摘要：该项目的目标是研究薄板和细丝在张力下扭曲时的大型形状变化，使用非侵入性3D激光和X射线扫描技术。该研究将结构的演变与其强度（远高于初始屈曲开始时和自接触后的扭转响应）联系起来。这项研究将集中在互补的超弹性材料，可以伸展显着相比，他们的大小，和不可伸展的材料，弯曲和塑性变形。内部结构的元素级测量将在物理模型方面进行分析，其中包括其几何形状和弹性响应。 对弹性体在大变形下的形状和强度的基本理解将影响各种材料的开发，包括功能性纱线和合成组织。研究结果将发表在同行评审的期刊上，并将增加凝聚态物理学领域的科学知识，并将通过互联网免费传播。该项目工作将支持本科生实习和研究生的论文研究工作。研究和指导活动将导致教育本科生和研究生追求在干相关学科的职业生涯，并推广活动，以K-12学生。技术摘要：该项目的目标是研究拓扑变换的薄片和细丝，因为它们是驱动崩溃和极端边界载荷下的自包装。将使用非侵入性3D激光和X射线扫描技术并表征表面曲率和能量学来获得作为所施加的边界载荷的函数的几何形状。这项研究将集中在互补的可逆和不可逆的应变转换材料的非微扰变形制度超出了经典弹性理论的范围。一个基于折纸运动学的细丝模型将被开发来解释自我折叠，扭曲本地化和螺旋缠绕的出现。损伤网络将与随机和空间相关的折叠算法进行分析，以确定的过程中，形状板奇异性，并在重复淬火下，使用扭矩测量他们的顺应性。 将探讨元件的弹性和接触力学的相对贡献，以理解纱线和组织的成形。研究结果将发表在同行评审的期刊上，并将增加凝聚态物理学，生物材料和快速成型领域的科学知识。研究和指导活动将导致教育多代学生群体追求STEM相关学科的职业生涯。该项目工作将支持本科生的实习和研究生的论文研究工作。该DMR资助支持在极端应力下的片和丝的拓扑变换研究，由凝聚态物理学（CMP）资助。该奖项反映了NSF的法定使命，并被认为是值得的。通过使用基金会的知识价值和更广泛的影响审查标准进行评估来提供支持。

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.