Timár G, Kun F, Carmona H A, Herrmann H J
Department of Theoretical Physics, University of Debrecen, P. O. Box 5, H-4010 Debrecen, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016113. doi: 10.1103/PhysRevE.86.016113. Epub 2012 Jul 27.
We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.
我们通过离散元模型研究了由非均质脆性材料制成的球形固体的冲击破碎情况。针对四种不同的系统尺寸进行了计算机模拟，在很宽的范围内改变冲击速度。我们进行了有限尺寸标度分析，以确定损伤 - 破碎相变的临界指数，并推导关于半径(R)和冲击速度(v(0))的标度关系。标度分析表明，幂律分布的碎片质量指数不依赖于冲击速度；近期模拟预测的指数明显变化可归因于截断的移动以及不可破碎离散单元的存在。我们的计算表明，破碎过程的特征时间尺度分别对冲击速度以及在损伤和破碎状态下与临界速度的距离具有幂律依赖性。发现总损伤量具有类似的行为，这与二维中观察到的对冲击速度的对数依赖性有很大不同。
