Abstract
Our research group has been interested at the ubiquitous, yet still poorly understood phenomenon of crumpling. In the past we have focused on designing high-pressure chambers for the purpose of crumpling thin sheets under di erent magnitudes of ambient pressure. In this thesis I shall try to attack the problem from a di erent front; that is, analytically and by Molecular Dynamics (MD) simulations. I also want to ask (1) how these mechanical and statistical properties derived from experiments come about? and (2) how they are a ected when two sheets of di erent composites are crumpled at the same time. Analytically, I can show that, within a simple \chessboard" model, how the average ridge lengths for each sheets evolve with the compaction, for which the average ridge length is positively related to bending modulus and inversely proportional to the density under the knowledge background from simulation. These results are consistent with the simulation results. One big advantage of studying MD is that we can get a clear physical picture for how the potential energy is allotted. We nd that, during cocumpling, the sheet with larger average facet takes the major blunt of external force and thus absorbs more energy in our simulations. In contrast to crumpling under an ambient pressure, I also check if the scaling relation persists when I crush the sheet unidirectionally. Unlike its 3-D counterpart, the mechanical properties of a 1-D crumpled ball depend more sensitively on the initial condition. More speci cally, the compaction of the precrumpled ball via a 3-D pressure a ects its later resistance in 1-D. We found that the force versus height relation consisted of three regions, similar to the 3-D case. Although the ball exhibits the scaling law in 3-D, the law does not exist when we change the nature of force to 1-D. We call this stage the rst region. When the height decreases, the scaling law appears and the power is between 0.25 to 0.35, somewhat larger than the exponent in 3-D for the same parameters of sheet. We reported possible connection between these regions and the change of inner structure. With the knowledge of these features, we considered an ellipsoid model that can predict both the power law and the right magnitude of exponent. Furthermore, the model revealed that the density is a better parameter than the height in the second region for the mechanical behavior. In the end, we investigated the density distribution of layers and found two kinds of distribution, which are dissimilar to that in 3-D crumpling. The nal part is a summary of conclusions and discussions on my previous e ort to investigate the quantized conductance of threadlike mercury. This was initially designed to combine my experience with the classic drop-breakup problem with the expertise of my labmate on quantized conductance in quantum point contacts. We hope to utilize the micro-size neck of mercury to investigate the correctness of report in the literature that the quantized conductance can persist in room temperature and pressure for liquid metal.