The study on performances of kernel types in solid dynamic problems by smoothed particle hydrodynamics

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.