Low-speed impacts between rubble piles modeled as collections of polyhedra, 2

We present the results of additional calculations involving the collisions of km-scale rubble piles. In new work, we used the Open Dynamics Engine (ODE), an open-source library for the simulation of rigid-body dynamics that incorporates a sophisticated collision-detection and resolution routine. We found that using ODE resulted in a speed-up of approximately a factor of 30 compared with previous code. In this paper we report on the results of almost 1200 separate runs, the bulk of which were carried out with 1000-2000 elements. We carried out calculations with three different combinations of the coefficients of friction η and (normal) restitution ε{lunate}: low (η = 0, ε{lunate} = 0.8), medium (η = 0, ε{lunate} = 0.5), and high (η = 0.5, ε{lunate} = 0.5) dissipation. For target objects of ∼1 km in radius, we found reduced critical disruption energy values Q_RD^* in head-on collisions from 2 to 100 J kg^-1 depending on dissipation and impactor/target mass ratio. Monodisperse objects disrupted somewhat more easily than power-law objects in general. For oblique collisions of equal-mass objects, mildly off-center collisions (b / b₀ = 0.5) seemed to be as efficient or possibly more efficient at collisional disruption as head-on collisions. More oblique collisions were less efficient and the most oblique collisions we tried (b / b₀ = 0.866) required up to ∼200 J kg^-1 for high-dissipation power-law objects. For calculations with smaller numbers of elements (total impactor n_i + target n_T = 20 or 200 elements) we found that collisions were more efficient for smaller numbers of more massive elements, with Q_RD^* values as low as 0.4 J kg^{- 1} for low-dissipation cases. We also analyzed our results in terms of the relations proposed by Stewart and Leinhardt [Stewart, S.T., Leinhardt, Z.M., 2009. Astrophys. J. 691, L133-L137] where m₁ / (m_i + m_T) = 1 - Q_R / 2 Q_RD^* where Q_R is the impact kinetic energy per unit total mass m_i + m_T. Although there is a significant amount of scatter, our results generally bear out the suggested relation.