应变率敏感球形固体冲击破碎的临界行为
Critical behavior for impact fragmentation of spherical solid bodies sensitive to strain rate
摘要：
本文研究了在三维环境中两个对应变率敏感的球形固体的碰撞破碎问题。我们使用量纲分析和光滑粒子流体动力学（SPH）方法的数值模拟来阐明这个问题。的工作的关键点是完全自相似的假设下考虑的问题，相对于有效应变率参数Eeff，这是通过数值模拟验证。因此，我们考虑对应于高速Eeff >> 1和低速Eeff <<1加载的两种情况。系统的大小可以由近似每个球体的SPH粒子的总数Ntot来表征。结果表明，对于有限体系，高速加载时的临界破碎速度大于低速加载时的临界破碎速度。随着系统尺寸的无限增加，这些速度变得相同。结果表明，临界碎裂速度与系统尺寸呈二次函数关系，即Vc ^2-Vc（inf）^2 ~ Ntot ^（1/3 nu），其中nu为关联长度指数.
英文摘要：
We consider the impact fragmentation of two spherical solid bodies sensitive to strain rate in a three-dimensional (3D) setting. We use both dimensional analysis and numerical simulations by smoothed-particle hydrodynamics (SPH) method to shed light on this problem. The key point of the work is the assumption of complete self-similarity of the problem under consideration with respect to the effective strain rate parameter Eeff, which is verified by numerical simulations. As a result we consider the two cases corresponding to the high-velocity Eeff >> 1, and low-velocity Eeff <<1 loading. The size of the system may be characterized by the total number of the SPH particles Ntot approximating each sphere. It is shown that for finite system the critical velocity of fragmentation at high-velocity loading exceeds that at low-velocity loading . With an unlimited increase in the system size these velocities become the same. It is shown that the critical velocity of fragmentation depend on the system size in a quadratic manner, i.e. Vc^2 -Vc(inf)^2 ~ Ntot ^(1/3nu) where nu is a correlation length exponent.
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