Application and Evaluation of the Material Point Method for Low-Velocity Asteroid Collisions Involving Large Deformations
The collisional lifetimes of asteroids larger than $\sim 10$ km in the present-day main belt are estimated to exceed the age of the solar system, suggesting that their shapes may preserve memories of the collisional environment in the primordial solar system. Recent studies performed systematic simulations of equal-mass and low-velocity ($50$--$400\,\mathrm{ms}^{-1}$) collisions between 50-km-radius asteroids using Smoothed Particle Hydrodynamics (SPH), identifying the impact conditions that produce irregular shapes. As an alternative approach, we here employ the Material Point Method (MPM), a particle-grid method well suited to large deformation of solids and free from tensile instability, and we assess its applicability to such systems by direct comparison with the established SPH results. We integrate a previously established rock model combined with a fracture model, the Tillotson equation of state, and Drucker-Prager friction, with the efficient non-associative Drucker-Prager plasticity solver originally developed for granular flows. We perform 135 collision simulations of equal-mass rocky asteroids spanning 15 impact velocities ($50$--$400\,\mathrm{ms}^{-1}$) and 9 impact angles ($5$--$45^\circ$), following the setup of the previous SPH simulations. The mass, axis ratio, and shape classification of the largest remnants closely reproduce the trends of the previous SPH simulations. Since most material transitions into a granular state early in the collision, this agreement appears to depend primarily on the validity of the frictional treatment of the granular material, rather than on the details of the fracture model. These results demonstrate the applicability of MPM to low-velocity asteroid collision simulations and support cross-validation between MPM- and SPH-based approaches.