The Impact of Effective Density and Compressive Strength on the Structure of Crumpled Paper Balls

Crumpling is the process whereby a sheet of paper undergoes deformation to yield a three-dimensional structure comprising a random network of ridges and facets with variable density. A regular sheet of paper can be easily teared and is very flimsy, yet when a sheet of paper is crumpled into a ball, the crumpled paper becomes much sturdier and has a large compressive strength, which is a material’s maximum compressive load divided by its cross-sectional area. Scientists have extensively studied this phenomenon due to its peculiar structure; however, the physics behind paper crumpling is not yet completely understood. In this study, we investigated the structure of crumpled paper in two ways. In the first part, we explored the effective density of crumpled paper balls and hypothesized the diameter cubed of a paper ball crumpled from a square paper sheet is directly proportional to the side length squared of the paper sheet. In the second part, we studied the relationship between the number of times an A4 piece of paper is crumpled and its compressive strength. We hypothesized that the more times a paper sheet is crumpled, the greater its compressive strength. Our results supported both of our hypotheses: The first experiment demonstrated there is a directly proportional relationship between the diameter cubed of the ball and the side length squared of the sheet. We discovered in the second experiment that there was a relatively strong linear relationship between the number of times a paper sheet is crumpled and its compressive strength.