二维晶格颗粒堆积中侧壁的压力分布与转向系数

颗粒物质是大量颗粒聚集在一起的软凝聚态物质, 其微观结构与宏观力学性质的联系非常复杂. 本文用实验的方法观测了二维竖直晶格堆积颗粒, 在竖直方向外加正压力作用下其侧壁的受力分布情况, 根据实验结果详细讨论和分析了颗粒体系中正压力的转向行为. 实验结果表明: 在缓慢压缩颗粒体系的过程中, 正压力的变化呈现非线性和线性两段不同的规律; 对于确定堆积结构的颗粒体系, 竖直方向施加的正压力通过颗粒力链转向, 且水平方向不同堆积高度处所受压力值不同, 中部的压力大于顶部和底部的压力; 转向系数k的饱和值随堆积角θ 的增大而减小. 对颗粒堆的几何结构与受力情况进行分析, 给出了转向系数与堆积角之间的数学表达式, 理论值与实验值符合较好.

Lateral pressure distribution and steering coefficient in two-dimensional lattice pile of granular material

Granular material is a kind of soft condensed matter, which gathers up a large number of particles, and the relation between its microstructure and macroscopic mechanical properties is very complex. In this paper, the lateral stress distribution of the two-dimensional vertically stacked lattice of granular material under a pressure in the vertical direction has been investigated experimentally. The steering behavior of the vertical pressure in a granular system is discussed and analyzed in detail based on the experimental results. Results show that in the process of slow compression, the vertical pressure increases slowly in a nonlinear form at first and gradually transforms into a linear increase. This phenomenon corresponds to the dynamic processes of friction-slip-extrusion. This kind of behavior is more significant in the particle system of the same size. In the initial stage of pressing, the vertical force of the stepping motor is mainly used to overcome the friction between the particles and the sliding friction between the particle and the wall. As the friction in the granular system is related to the geometry of the particulate deposits, the material of particles, the roughness of the wall surface, and other relevant factors, the front-end of vertical pressure displays nonlinear characteristics. Continuing the squeeze and push forward, a force chain is formed among particles through self-organization. The vertical force is mainly used to overcome the elastic pressing force between the particles and the force to the wall, so later on the vertical pressure performs linear growth. For the system of particles with an established packed structure, the vertical pressure applied in the vertical direction steers along the force chain between the particles, and the value of horizontal pressure is different at different stacking heights. That is, the pressure in the middle is greater than that at the top and the bottom. The saturated value of steering coefficient k decreases with the stacking angle θ. As the stacking angle increases, the vertical component of the stress becomes more pronounced than its horizontal component. The expression of steering coefficients against stacking angle has been obtained through careful analysis of the geometrical structure and the force distribution of the granular pile, and the theoretical value fit well with the experimental results.