Stress and Failure Analysis of Rapidly Rotating Asteroid (29075) 1950 DA

Rozitis et al. recently reported that near-Earth asteroid (29075) 1950 DA, whose bulk density ranges from 1.0 g/cm3 to 2.4 g/cm3, is a rubble pile and requires a cohesive strength of at least 44 Pa to 74 Pa to keep from failing due to its fast spin period. Since their technique for giving failure conditions required the averaged stress over the whole volume, it discarded information about the asteroid's failure mode and internal stress condition. This paper develops a finite element model and revisits the stress and failure analysis of 1950 DA. For the modeling, we do not consider material-hardening and softening. Under the assumption of an associated flow rule and uniform material distribution, we identify the deformation process of 1950 DA when its constant cohesion reaches the lowest value that keeps its current shape. The results show that to avoid structural failure the internal core requires a cohesive strength of at least 75 Pa - 85 Pa. It suggests that for the failure mode of this body, the internal core first fails structurally, followed by the surface region. This implies that if cohesion is constant over the whole volume, the equatorial ridge of 1950 DA results from a material flow going outward along the equatorial plane in the internal core, but not from a landslide as has been hypothesized. This has additional implications for the likely density of the interior of the body.