Executive Summary of Modeling the Motion of Falling Intruders

Modelling the Motion of Falling Intruders in Granular Materials in Three Dimensions

        Most of the world consists of one of three types of matter: solid, liquid, and gas. When these forms of matter interact, we get the interesting reactions that make up everything on Earth. One such form of interaction exists in materials known as granular materials. Granular materials are collections of small (but still visible to the naked eye) solid particles which interact with each other and the environment around them. Some common examples include sand, soil, and gravel. Although these materials consist only of solid particles, they exhibit properties of solids, liquids and gases. For example imagine we have sand in a box. While the sand sits in the box, it acts much like a solid. You can try and compress the sand down, but it will act like a solid and resist the compression. If you then pick the box up and tilt it on its side, the sand begins to flow out of the box, much like a liquid would.

        Another interesting property of granular materials lies in how the material acts when affected by an intruder, any sort of solid mass trying to penetrate into the material. Much of past work in studying the effects of impact in granular materials has only been done in two dimensions. Since we live in a three-dimensional world, this study worked to extend the models produced from the two-dimensional study to three-dimensions.

        Over the course of the study, the analysis of the data gave us unexpected results. Typically, when studying impacts in granular materials, a velocity-squared model is used, where the acceleration experienced by an intruder is roughly proportional to the square of its velocity. Our data does not show this, however it suggests that the velocity-squared model may still work, with altered coefficients. There could also be potential need for the development of a completely new model. The necessity of this model is still being determined.