Application of an improved contact algorithm for penetration analysis in SPH

A numerical algorithm to analyze an elasto-plastic contact problem using the smoothed particle hydrodynamics (SPH) method is proposed. In order to solve the contact problem with SPH when both bodies are deformable, a variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method. Methods to find the boundary particles and to determine the boundary normal vector are reviewed to apply to the contact algorithm. In calculating the actual penetration and penetration rate, a method that can determine the actual normal boundary vector through the contact relationship with a contact surface is proposed. A numerical simulation is conducted to validate the proposed method in cylindrical coordinates. A steel ball 10 mm in diameter impacting a thin steel plate of 1 mm thickness at a high velocity such as 200 m/s is chosen to verify that the contact algorithm can be applied to the penetration problem. The final shape results obtained by the proposed contact algorithm are more similar to the experimental results than the conventional SPH analysis results.