Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density “random-close packing” polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.

The scope of this project is a combination of material science engineering and mechanical engineering. Overall, the main goal of this project is to develop a lightweight concrete that maintains its original strength profile. Initial research has shown that a plastic-concrete composite could create a more lightweight concrete than that made using the typical gravel aggregate for concrete, while still maintaining the physical strength that concrete is known for. This will be accomplished by varying the amount of plastic in the aggregate. If successful, this project would allow concrete to be used in applications it would typically not be suitable for.<br/>After testing the strength of the concrete specimens with varying fills of plastic aggregate it was determined that the control group experienced an average peak stress of 2089 psi, the 16.67% plastic group experienced an average peak stress of 2649 psi, the 33.3% plastic group experienced an average peak stress of 1852 psi, and the 50% plastic group experienced an average stress of 924.5 psi. The average time to reach the peak stress was found to be 12 minutes and 24 seconds in the control group, 15 minutes and 34 seconds in the 16.7% plastic group, 9 minutes and 45 seconds in the 33.3% plastic group, and 10 minutes and 58 seconds in the 50% plastic group. Taking the average of the normalized weights of the cylindrical samples it was determined that the control group weighed 14.773 oz/in, the 16.7% plastic group weighed 15 oz/in, the 33.3% plastic group weighed 14.573 oz/in, and the 50% plastic group weighed 12.959 oz/in. Based on these results it can be concluded that a small addition of plastic aggregate can be beneficial in creating a lighter, stronger concrete. The results show that a 16.7% fill ratio of plastic to rock aggregate can increase the failure time and the peak strength of a composite concrete. Overall, the experiment was successful in analyzing the effects of recycled plastic aggregate in composite concrete. <br/>Some possible future studies related to this subject material are adding aluminum to the concrete, having better molds, looking for the right consistency in each mixture, mixing for each mold individually, and performing other tests on the samples.

The scope of this project is a combination of material science engineering and<br/>mechanical engineering. Overall, the main goal of this project is to develop a lightweight<br/>concrete that maintains its original strength profile. Initial research has shown that a<br/>plastic-concrete composite could create a more lightweight concrete than that made using the<br/>typical gravel aggregate for concrete, while still maintaining the physical strength that concrete is<br/>known for. This will be accomplished by varying the amount of plastic in the aggregate. If<br/>successful, this project would allow concrete to be used in applications it would typically not be<br/>suitable for.<br/>After testing the strength of the concrete specimens with varying fills of plastic aggregate<br/>it was determined that the control group experienced an average peak stress of 2089 psi, the<br/>16.67% plastic group experienced an average peak stress of 2649 psi, the 33.3% plastic group<br/>experienced an average peak stress of 1852 psi, and the 50% plastic group experienced an<br/>average stress of 924.5 psi. The average time to reach the peak stress was found to be 12 minutes<br/>and 24 seconds in the control group, 15 minutes and 34 seconds in the 16.7% plastic group, 9<br/>minutes and 45 seconds in the 33.3% plastic group, and 10 minutes and 58 seconds in the 50%<br/>plastic group. Taking the average of the normalized weights of the cylindrical samples it was<br/>determined that the control group weighed 14.773 oz/in, the 16.7% plastic group weighed 15<br/>oz/in, the 33.3% plastic group weighed 14.573 oz/in, and the 50% plastic group weighed 12.959<br/>oz/in. Based on these results it can be concluded that a small addition of plastic aggregate can be<br/>beneficial in creating a lighter, stronger concrete. The results show that a 16.7% fill ratio of<br/>plastic to rock aggregate can increase the failure time and the peak strength of a composite<br/>concrete. Overall, the experiment was successful in analyzing the effects of recycled plastic<br/>aggregate in composite concrete.<br/>Some possible future studies related to this subject material are adding aluminum to the<br/>concrete, having better molds, looking for the right consistency in each mixture, mixing for each<br/>mold individually, and performing other tests on the samples.