局部约束模式对单颗粒破碎强度的影响

为了研究不同约束模式对单颗粒破碎的影响，通过改变颗粒的接触状态（接触点个数、接触角度）设计一系列约束模式.对描述颗粒接触状态的二维矩阵进行奇异值分解（SVD），得到量化颗粒约束状态的特征值.基于Voronoi图生成试样的随机不规则网格，在连续-离散耦合分析方法（FDEM）的基础上建立颗粒模型，研究颗粒的破碎强度和破碎形式与约束模式之间的关系，建立考虑颗粒约束模式的破碎阈值模型.通过大量的数值模拟结果可以看出，在颗粒破碎过程中，靠近竖直加载轴线的约束部位出现初始裂纹，并逐渐发展成为宏观贯穿裂缝，继而圆周侧向约束部位出现向顶部或底部约束部位扩展的裂纹.颗粒接触点或者配位数越多，SVD分解得到的平均奇异值越大，颗粒破碎阈值越高.在接触点或者配位数相同的情况下，约束模式对应的平均奇异值越高或偏状态程度越低，颗粒抵抗破碎的能力越强.
Abstract: A series of constraint modes were designed by changing the contact state of the particle, including the coordination number and contact position, in order to analyze the effects of local constraints patterns on fragmentation of single grain. The singular value decomposition (SVD) was applied to the two-dimensional matrix representing the contact state of particles, and the obtained singular values could make the constraint modes quantified. The mesh topology based on Voronoi diagram was applied to simulate the heterogeneous structure of particles. Plenty of numerical simulations of two-dimensional particle crushing was conducted by using the combined finite-discrete element method (FDEM) in order to reveal the effects of constraint modes on the failure strength and the crushing forms. The fragmentation threshold model was constructed. The numerical results show that during particle crushing, initial cracks appear near the loading axis and ultimately splitting the specimen. Other cracks originate from lateral contacts and generally reach the top or bottom contact. Higher mean singular value and enhanced critical force are resulted with increasing coordination number. With the same coordination number, the fragmentation threshold of grains gets higher as the mean singular value increases or the difference between the singular values decreases.