As the earliest meshless method, smoothed particle hydrodynamics (SPH) has been applied in solid dynamics because of its great potentials in simulating extremely large deformations. In terms of the essence of SPH, it uses a kernel function for numerical approximations. Some studies demonstrate mathematically that the types of the kernel function directly influence the stability and overall accuracy of SPH simulation. However, less attention is paid to the influences derived from kernels, particularly on simulating dynamic solids problems by SPH. In addition, some researches introduce that there are strong relations between SPH kernels and tensile instability which is one of the shortcomings in SPH method, a kind of particles clumping phenomenon probably leading to some unphysical cracks when the solid material is largely stretched or compressed. At present, no method exists to completely avoid these instabilities, although a few corrections like artificial viscosity, artificial stress, corrective SPH or the Godunov-type SPH have been proposed.In this paper, the performances of SPH method with different kernels are studied, including classical types and several new ones proposed recently. Combined with some corrected techniques, the suitability of these kernels in SPH method is discussed in solid dynamic problems like bending deformation of elastic beam and some tests about elastic–plastic deformation in impact problems.

作为最早的无网格方法，平滑粒子流体动力学（SPH）已被应用在固体动力学中，因为它在模拟极大变形方面具有巨大的潜力。就SPH的本质而言，它使用内核函数进行数值逼近。一些研究从数学上证明了核函数的类型直接影响SPH仿真的稳定性和整体准确性。但是，对内核派生的影响的关注较少，特别是在通过SPH模拟动力学固体问题上。另外，有研究表明，SPH核与拉伸不稳定性之间存在很强的联系，这是SPH方法的缺点之一。当固体材料大量拉伸或压缩时，这种颗粒团聚现象很可能导致一些非物理裂纹。尽管已经提出了一些修正措施，如人工粘度，人工应力，修正性SPH或Godunov型SPH，但目前还没有完全避免这些不稳定性的方法。本文研究了不同内核的SPH方法的性能，包括古典类型和最近提出的几种新类型。结合一些校正的技术，讨论了SPH方法中这些内核的适用性，以解决诸如弹性梁弯曲变形之类的固体动力学问题以及有关冲击问题中弹塑性变形的一些测试。研究了不同内核的SPH方法的性能，包括经典类型和最近提出的几种新类型。结合一些校正的技术，讨论了SPH方法中这些内核的适用性，以解决诸如弹性梁弯曲变形之类的固体动力学问题以及有关冲击问题中弹塑性变形的一些测试。研究了不同内核的SPH方法的性能，包括经典类型和最近提出的几种新类型。结合一些校正技术，讨论了SPH方法中这些内核的适用性，以解决诸如弹性梁弯曲变形之类的固体动力学问题，以及有关冲击问题中弹塑性变形的一些测试。