图 1  (a) “六足体”颗粒示意图, 其中紫色部分为圆柱体, 粉色部分为半球帽; (b)实验装置图; (c) CT拍摄示意图; (d)“六足体”颗粒堆积的 CT 切片图

Fig. 1.  (a) Schematic diagram of “hexapod” particles (the purple part is a cylinder, the pink part is a hemispherical cap); (b) diagram of the experimental setup; (c) schematic diagram of CT scan; (d) CT slice of “hexapod” particle packing.

图 2  (a)不同振动加速度$\varGamma $条件下, 颗粒堆积的压实曲线及KWW拟合曲线(实线); (b)弛豫时间$\tau $与振动加速度$\varGamma $的关系图; (c)稳态体积分数$\varPhi {\text{f}}$与振动加速度$\varGamma $的关系图

Fig. 2.  (a) Compaction curves of various tapping intensities $\varGamma $and the corresponding KWW fits (lines); (b) relaxation time $\tau $ as a function of tapping intensities $\varGamma $; (c) steady-state packing fraction $\varPhi {\text{f}}$ as a function of tapping intensities $\varGamma $.

图 3  (a)近邻“六足体”颗粒臂之间的表面间距$\Delta r{\text{arm}}$的概率分布及高斯拟合曲线(实线); (b)接触数$Z$与接触阈值$\delta {\text{th}}$的函数关系图

Fig. 3.  (a) Probability distribution function (PDF) of the surface distance $\Delta r{\text{arm}}$ between the arms of neighboring hexapods and the Gaussian fitting curve (solid line); (b) the contact number $Z$ as a function of the contact threshold $\delta {\text{th}}$.

图 4  (a)不同振动加速度$\varGamma $时, 接触数$Z$随振动次数$t$的变化曲线; (b)不同振动加速度$\varGamma $时, 接触数$Z$随体积分数$\varPhi $的变化曲线

Fig. 4.  (a) The contact $Z$ number as a function of the tapping number $t$ under different tapping intensities $\varGamma $; (b) the contact number $Z$ as a function of the volume fraction $\varPhi $ under different tapping intensities $\varGamma $.

图 5  (a)接触距离$d{\text{con}}$示意图. 图中白色实心圆表示颗粒中心, 绿色实心圆表示颗粒接触位置, 黑色实线表示过颗粒中心的颗粒臂轴线; (b)接触距离$d{\text{con}}$的概率分布图; (c)不同振动加速度$\varGamma $下, 平均接触距离$\left\langle {d{\text{con}}} \right\rangle $随振动次数$t$的变化曲线; (d)不同振动加速度$\varGamma $下, 平均接触距离$\left\langle {d{\text{con}}} \right\rangle $随体积分数$\varPhi $的变化曲线

Fig. 5.  (a) Schematic diagram of the contact distance $d{\text{con}}$. The white solid circle represents the center of the particle, the green solid circle represents the contact position of the particles, and the black solid line represents the axis of the particle arm passing through the particle center; (b) probability distribution function (PDF) of the average contact distance $\left\langle {d{\text{con}}} \right\rangle $; (c) the contact distance $d{\text{con}}$ as a function of the tapping number $t$ under different tapping intensities $\varGamma $; (d) the average contact distance $\left\langle {d{\text{con}}} \right\rangle $ as a function of the packing fraction $\varPhi $ under different tapping intensities $\varGamma $.

图 6  (a) 3种接触(cs接触、cc接触、ss接触)类型示意图. 紫色部分为圆柱体, 粉色部分为半球帽, 绿色实心圆表示接触点; (b)不同振动加速度$\varGamma $下, 3种接触类型所占比例随振动次数$t$的变化曲线; (c)不同振动加速度$\varGamma $下, 3种接触类型所占比例随稳态体积分数$\varPhi $的变化曲线

Fig. 6.  (a) Schematic diagram of three contact types (cs contacts, cc contacts, ss contacts), the purple part is the cylinder, the pink part is the hemispherical cap, and the green solid circle represents the contact point; (b) ratios of three contact types as a function of the tapping number $t$ under different tapping intensities $\varGamma $; (c) ratios of three contact types as a function of the steady-state packing fraction $\varPhi $ under different tapping intensities $\varGamma $.