论文标题
对应变率敏感的球形固体的影响碎片的临界行为
Critical behavior for impact fragmentation of spherical solid bodies sensitive to strain rate
论文作者
论文摘要
我们考虑在三维（3D）设置中对应变率敏感的两个球形固体的影响碎片。我们通过平滑的粒子流体动力学（SPH）方法使用尺寸分析和数值模拟来阐明此问题。工作的关键点是假设在有效应变率参数eeff方面考虑了所考虑的问题的完全自相似性，这是通过数值模拟验证的。结果，我们考虑了与高速eeff >> 1相对应的两种情况，而低速eeff << 1加载。系统的大小可能以近似于每个球体的SPH颗粒的总数NTOT的总数。结果表明，对于有限系统，高速载荷下碎片的临界速度超过了低速载荷下的临界速度。随着系统尺寸无限增加，这些速度变得相同。结果表明，碎片的临界速度以二次的方式取决于系统大小，即vc^2 -vc（inf）^2〜ntot^（1/3nu），其中nu是相关长度指数。
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.
