Application of SPH in stress wave simulation

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 particle 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 dimensionless 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 simulation result of SPH.