Application of SPH Method for Problem of Rock Penetration within the Wide-Ranged Velocity

The smoothed particle hydrodynamics (SPH) method is used to simulate the deformation of penetration of granite at large strain and high strain rates. In order to describe the nonlinear deformation and failure characteristics of the projectile and target, the Holmquist-Johnson-Cook (HJC) constitutive model, damage model, Johnson-Cook (J-C) constitutive model and Grüneisen equation of state for granite are introduced, in which the projectile and the fortifications are discretized into Lagrangian particles. In simulation of three-dimensional penetration process of granite targets by self-made program at the speed from 0 m/s to 4000 m/s, we compare and analyzes the penetration results of steel balls under different projectile conditions. The curve of the penetration depth with the penetration velocity is fitted in solid penetration, semi-fluid penetration and fluid invasion. The numerical results show that the penetration depth increases with the increase of the penetration velocity in the solid penetration interval (${v_0} < 1421\;\,{\rm{m}}/{\rm{s}}$). A decreasing trend is shown in the semi-fluid penetration interval ($1421\;{\rm{m}}/{\rm{s}} \leqslant {v_0} \leqslant 1700\;{\rm{m}}/{\rm{s}}$), while an increasing trend is shown in the fluid penetration interval ($1421\;{\rm{m}}/{\rm{s}} < {v_0} <1700\;{\rm{m}}/{\rm{s}}$) and gradually tended to reach the peak.