DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING
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摘要: 颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k−Γ分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.Abstract: Granular material is a complex multi-body interaction system which is composed of a large number of discrete particles and their surrounding free volume. Although the correlation between free volume and the mechanical properties as well as the deformation characteristics of granular materials has been proved, the local free volume of non-spherical particles is not fully understood at present due to the difficulties in characterizing. In this paper, the combined finite and discrete element method (FDEM) is used to simulate the triaxial tests of ellipsoidal particles with different principal axis lengths, and the Set Voronoi tessellation method is applied to construct the Voronoi cells of the particles during shearing. The statistical distribution and evolution of the local free volume of the granular systems during shearing are analyzed, and the influence of particle shape on the evolution of free volume is studied. Our results show the anisotropy of Voronoi cells gradually increases during shearing, and the degree of anisotropy increase will be intensified with the increase of particle shape asphericity, which means the granular assembly with a larger asphericity will experience more intense rearrangement during shearing. The local void ratio of ellipsoidal particle systems with different asphericity statistically complies with a k−Γ distribution, which is controlled by the global void ratio of granular assembly and not affected by particle shape and shear state. The local void ratio fluctuations follow an asymmetric laplace distribution (ALD), and its asymmetric parameter which has a linear relationship with the global void ratio of granular assembly describes the competition between contraction and dilatation of local free volume.
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Key words:
- ellipsoidal particle /
- Voronoi cell /
- free volume /
- anisotropy /
- local void ratio /
- local void ratio fluctuation
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图 4 不同非球度的椭球颗粒偏应力−轴向应变
Figure 4. Curves of deviatoric stress versus axial strain for ellipsoidal particles with different asphericity
图 5 不同非球度的椭球颗粒体积应变−轴向应变
Figure 5. Curves of volumetric strain versus axial strain for ellipsoidal particles with different asphericity
图 6 Set Voronoi 剖分二维示意图
Figure 6. Two-dimensional illustration of Set Voronoi tessellation
图 8 不同非球度的椭球颗粒在不同加载阶段的Voronoi元胞球度概率密度分布
Figure 8. Probability density distributions of sphericity of Voronoi cells at the different loading states for ellipsoidal particles with different asphericity
图 9 不同非球度的椭球颗粒在临界状态的Voronoi元胞球度概率密度分布
Figure 9. Probability density distributions of sphericity of Voronoi cells at critical state for ellipsoidal particles with different asphericity
图 10 临界状态下Voronoi元胞球度与颗粒形状参数
$\alpha $ 的关系Figure 10. Relationship between Voronoi cell sphericity and shape parameter
$\alpha $ of particle at critical state
图 11 不同非球度的椭球颗粒在不同加载阶段的局部孔隙比概率密度分布
Figure 11. Probability density distributions of local void ratio at the different loading states for ellipsoidal particles with different asphericity
图 12 不同非球度的椭球颗粒在全局孔隙比相同时局部孔隙比概率密度分布
Figure 12. Probability density distributions of local void ratio at the states as same global void ratio for ellipsoidal particles with different asphericity
图 13 局部孔隙比的标准差与全局孔隙比的关系
Figure 13. Relationship between standard deviation of local void ratio and global void ratio
图 14 不同非球度的椭球颗粒试样在不同加载阶段的局部孔隙比波动概率密度分布
Figure 14. Probability density distributions of local void ratio fluctuations at the different loading states for particles with different shapes
图 15 非对称参数
$\kappa $ 与全局孔隙比的关系Figure 15. Relationship between asymmetric parameter
$\kappa $ and global void ratio表 1 FDEM数值模拟细观参数
Table 1. Parameters used in the FDEM simulation
Parameter Unit Value density kg/m3 2600 friction coefficient − 0.5 normal penalty N/m3 4 × 1011 tangential penalty N/m3 4 × 1011 Young’s modulus GPa 40 Poisson’s ratio − 0.2 normal critical damping fraction − 0.03 tangential critical damping fraction − 0.03 
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