Cárdenas-Barrantes Manuel, Cantor David, Barés Jonathan, Renouf Mathieu, Azéma Emilien
LMGC, Université de Montpellier, CNRS, Montpellier, France.
Laboratoire de Micromécanique et Intégrité des Structures (MIST), UM, CNRS, IRSN, France.
Soft Matter. 2022 Jan 5;18(2):312-321. doi: 10.1039/d1sm01241j.
This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.
本文利用三维非光滑接触动力学模拟，分析了由软（弹性）球形颗粒组成的组件在超过堵塞状态后的压实行为。随着围压增加，通过堆积分数、配位数以及颗粒内冯·米塞斯应力分布的演变来表征颗粒组件。堆积分数增加并趋向于接近1的最大值，平均配位数随着堆积分数的平方根增加。随着围压增加，观察到从具有指数尾部剪切应力分布的颗粒状材料向以高斯型剪切应力分布为特征的连续状材料的转变。我们推导了一个方程，该方程描述了堆积分数随外加压力的演变。这个基于颗粒应力张量的微观力学表达式、小变形下赫兹接触定律的极限以及堆积分数与颗粒配位数之间的幂律关系的方程，从堵塞点到非常高的密度都能提供良好的预测，而无需调整任何参数。
