Crumpling a Thin Sphere

• Main Authors: Fan-Jiang, Hung-Jie, 范姜泓杰
• Other Authors: Hong, Tzay-Ming
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/s8sa87

碩士 === 國立清華大學 === 物理學系 === 106 === 　　Crumpled membranes exhibit many interesting mechanical and statistical properties. However, researchers, including us, have long focused on flat sheets and did not second-guess whether an object that carries extrinsic curvature (and/or closed, i.e., without boundaries) may behave differently when crushed. We use Molecular Dynamics (MD) simulation to study the crumple process of a thin sphere in three dimensions. 　　The first property we measure is how the ratio of bending energy and stretching energy changes with volume density of the crumpled ball. In sheet case, it can be proved to 5 but the result of sphere is 1. The same part of sheet and sphere is that the ratio of bending energy and stretching energy will decay obviously in many-body interaction stage. Second is the relation between external force and volume density. The most different part is power law can not be seen for sphere case. Third is how the average total energy stored in each crease scales with the ridge length. The power of sheet is 1/3 and sphere is 1. 　　Based on MD result, Kite model is no longer suit for sphere. The reason is the difference of deformation of sheet is ridge, but the deformation of sphere is pit.