A simplified linear consistency kernel function in SPH method

Smoothed Particle Hydrodynamics (SPH) is a relatively new technique for simulating the dynamic response of solids, especially for high velocity impact and fracture problem. However, closer examination of SPH reveals some severe problems. The major difficulties are: (1) tensile instability; (2) zero-energy mode; (3) boundary deficiency; (4) less accuracy. One solution to these major difficulties with SPH is to improve the consistency of the kernel function. Based on the Reproducing Kernel Particle Method (RKPM), the concept of the proposed simplified linear consistency is introduced. The most attractive feature of the simplified linear consistency is the ease and cheapness of doing 3D calculation. One contribution of this paper is to show clearly the accuracy of solution gradually improved by increasing the order of the consistency. Simple 3D impacting models are established with different geometries and higher accurate results are obtained by using higher consistency kernel functions. Other features as numerical convergence, computational efficiency, etc. and some considerations of the simplified linear consistency kernel function are also discussed.