Abstract
In this thesis, we use molecular dynamics (MD) simulation to study crumpled membranes. Although it exists in our everyday life, there are still many mysteries in the properties related to crumpling that are starting to be unraveled in recent years. We use MD to study the mechanical properties of a thin sheet being crumpled under an ambient pressure. The way we proceed is to confine the fictitious sheet by a spherical shell under an external pushing force. In our MD, we use a triangular lattice model in which particles are simulated by lattice points and form a two-dimensional membrane. Two previous Nature-Material papers have confirmed a scaling law between the radius and external force and concluded that the power of the relation was universal - independent of materials, thickness and size of the sheet. Through real experiments, our group have upheld the scaling law, except that we found the exponent to vary with different made of the sheet. Why did the previous renowned workers fail to find this? If they had made a mistake, is there any other conclusion of theirs that will be cast into doubt? To explain all these questions, we set out to redo the MD simulation ourselves. Simulations allow us to measure and observe many physical quantities that is hard or impossible to obtain in experiments. For example, we can know (1) how the ridges corroborate in their formation to resist against the external force, (2) the statistical distribution of ridge length, (3) how the stored energy varies with the ridge length, (4) all the questions above for the case when two sheets of different made are crumpled together (we have a lab mate, Ming-Han Chou, who is in charge doing this experiment so that we can compare our results). To obtain the above mentioned distributions, I wrote a program that enables me to build the net of ridges fast and easily. With the help of this program, the inaccuracy of the locations and lengths of ridges from Watershed Algorithm was minimized. In the end, we found the energy to be linearly proportional to the ridge length, instead of having a one-third power as Professor Witten claimed. Besides, the average ridge length is found to be proportional to the inverse of the density. We proposed a simple model which can satisfactorily explain all our findings.