Matsuda Yu, Fukui Satoru, Kamiya Ryota, Yamaguchi Hiroki, Niimi Tomohide
Department of Modern Mechanical Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo 169-8555, Japan.
Department of Micro-Nano Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi 464-8603, Japan.
Phys Rev E. 2019 Mar;99(3-1):032906. doi: 10.1103/PhysRevE.99.032906.
We investigated the low speed impact on a granular bed by a hydrogel sphere and especially focused on the resultant crater diameter. Though the crater diameter depends only on the impact kinetic energy for the solid sphere impact cratering, it also depends on the elastic energy for the hydrogel sphere. The hydrogel sphere impact cratering is classified into two dynamics: small and large indentation of the sphere. For the small indentation, the crater diameter is proportional to the 1/4 power of the energy for ejecting granular materials, which is calculated by substituting the elastic energy stored in the sphere from the impact kinetic energy. Considering the force balance between the inertial force and the indentation, we derived the relation between the impact kinetic energy, Young's modulus, and the crater diameter. In the large limit of Young's modulus, the relation leads to the 1/4 power law observed in solid sphere impact. The dependency of Young's modulus on the crater diameter for the large indentation of the sphere is larger than the impact with small indentation.
我们研究了水凝胶球体对颗粒床的低速撞击，并特别关注由此产生的弹坑直径。虽然对于固体球体撞击形成弹坑而言，弹坑直径仅取决于撞击动能，但对于水凝胶球体，它还取决于弹性能。水凝胶球体撞击形成弹坑可分为两种动力学情况：球体的小凹痕和大凹痕。对于小凹痕，弹坑直径与用于喷射颗粒材料的能量的1/4次方成正比，该能量通过从撞击动能中减去球体中存储的弹性能来计算。考虑到惯性力和凹痕之间的力平衡，我们推导出了撞击动能、杨氏模量和弹坑直径之间的关系。在杨氏模量的大极限情况下，该关系导致了在固体球体撞击中观察到的1/4次方定律。对于球体的大凹痕，杨氏模量对弹坑直径的依赖性大于小凹痕撞击的情况。
