Improved Smoothed Particle Hydrodynamics for the Three-Dimensional Solid Impact Problems

Total Lagrangian-Smoothed Particle Hydrodynamics (TL-SPH) method is an important method to improve the tensile instability of traditional SPH, but it still faces some defects, such as insufficient accuracy at boundary region, difficulty in obtaining damage and applying interface conditions. Therefore, the high-order TL-SPH is applied for the elastic–plastic solid. A damage model is proposed by adaptively transforming the type of kernel function. Furthermore, a Riemann contact algorithm is introduced for different solids. The advantages of the methods in improving tensile instability and simulating damage are verified by the cases of the plates and the notched beams with an impact load.