Impact on dense gravitationally compacted assemblies of particles leads to complex dynamics of the impactor and of the granular particles themselves. The details of the intruder’s dynamics, and of the causal connection between this dynamics and the material response has been a subject of extensive research during the last decade. In this project, we use topological tools to analyze the results of physical experiments carried out with photoelastic particles at Duke University. Photoelasticity allows to visualize (using high-speed imaging) the structure of the force/stress field in the granular assembly during impact. Novel computational topology methods allow for quantification of the force/stress field that develops during an impact. Such quantification has been carried out, leading to much better understanding of the particulate material response to impact. The Capstone project has continued into a summer research project for one of the participating students, Tadanaga Takahashi, supported by an NSF REU supplement. The instructor acknowledges useful input by Abe Clark, PhD, Yale University, and by the collaborating groups from Rutgers and Duke Universities, led by Profs. K. Mischaikow and R. Behringer, respectively. The results from this project were published in Phys. Rev E, 97, 012906 (2018).
Force field developing in particulate systems exposed to impact (experiments carried out at Duke University under guidance by Prof. R. Behringer).
Processed images showing force field in the granular sample together with topological measures resulting from persistence topology, total photoelastic intensity and intruder’s acceleration.