On March 16th, 2018, Prof. Caishan Liu from the Department of Aeronautics & Astronautics, College of Engineering (COE), has published a paper entitled “Archimedes’ law explains penetration of solids into granular media” on Nature Communications (DOI: 10.1038/s41467-018-03344-3), which reported their latest research progress in characterizing the dynamic mechanical properties of granular materials.
The ubiquity of dense granular matter in nature and the important role it plays in human society cannot be overestimated. Studies on its mechanical properties are not only one of the important scientific issues in fundamental science, but also closely related to multiple applications, e.g., locomotion of terrestrial animals, robots working on granular substrates, impact protection engineering, geological disaster protection, etc. In response to the needs of the lunar exploration project in China, Caishan Liu’s research group has systematically carried out studies on the dynamic mechanical properties of granular materials and their spiral transmission dynamics in recent years. These researches not only supported the realization of China's aerospace engineering, but also made some significant progresses in the theoretical study of granular mechanics.
The research that published on Nature Communications confirmed that granular materials have the typical characteristics of complex fluids. Using a range of experiments, they showed that the relation between the penetration depth of an object and the force resisting it, transiently nonlinear and then linear, is scalable to a universal form. The gradient of the steady-state part, kø, which depends only on the medium’s internal friction angle, is calculated theoretically. They further showed that the intrusion of any convex solid shape satisfies a modified Archimedes’ law with the coefficient kø. This theoretical result can be verified by both their own experiments and experimental results of the existing literature.
Figure 1. The theoretical model of an object intruding granular material. There exists a conical stagnant zone (pink region AOB) ahead of the intruder, and a plastic region (cyan region) around them.
Figure 2. Left: Dimensionless pressure–depth curves for the different granular materials (glass beads, millet and sand). Right: Theoretical prediction of kø.
This result has already been applied to designing the drilling process in the lunar exploration project of China. The first and second authors of the article were Ph.D. students Wenting Kang and Yajie Feng, from COE, Peking University. The corresponding author was Professor Caishan Liu and co-author Professor R. Blumenfeld from Cambridge University.
The study was funded by the National Natural Science Foundation of China and the Satellite Research Institute of the China Academy of Aeronautics and Astronautics Fifth Institute (the moon exploration drilling project).