应力波数值计算中的SPH方法

Application of SPH in stress wave simulation

对一维波动方程的SPH(smoothed particle hydrodynamics)格式和有限差分格式进行比较,并采用SPH法模拟了一维应力/应变波,获得1个可衡量SPH法模拟应力波准确性的重要指标。结果表明,SPH法模拟应力波传播中采用的光滑长度必须不小于粒子间距;采用B-样条核函数和高斯型核函数能够获得良好的应力波图像,而二次型核函数不能,因此二次型核函数不适用于冲击动力学的数值计算。

Obtaining accurate waveforms is significant in impact mechanics numerical calculation. This paper is to analyze how the kernel functions and smooth length affect the result of stress wave simulation. The SPH （smoothed particle hydrodynamics） formulations with different kernel functions and smooth lengths of one dimensional wave equation was compared with the finite difference formulation, which was derived in this paper. One dimensional stress and strain waves were simulated using the SPH method with different kernel functions and smooth lengths, and waveforms were gained accurately by B-spline and Gaussian kernels when the smooth length was equal to or greater than the parti- cle interval. The wave velocity obtained by the quadratic kernel is below the theoretical value, no matter what the smooth length is. A parameter was deduced in this paper as roughly equal to the di- mensionless wave velocity. Several conclusions were drawn. Firstly, the smooth length is equal to or greater than the particle interval, which is the necessary prerequisite for accurate stress wave simulation with SPH. Then, the quadratic kernel is not suitable in impact mechanics numerical calculation. Finally, the parameter deduced in this paper is a significant index to evaluate the stress wave simula- tion result of SPH.