  Many asteroids are rubble piles with irregular shapes. While the irregular
shapes of large asteroids may be attributed to collisional events, those of
small asteroids may result from not only impact events but also rotationally
induced failure, a long-term consequence of small torques caused by, for
example, solar radiation pressure. A better understanding of shape deformation
induced by such small torques will allow us to give constraints on the
evolution process of an asteroid and its structure. However, no quantitative
study has been reported to provide the relationship between an asteroid's shape
and its failure mode due to its fast rotation. Here, we use a finite element
model (FEM) technique to analyze the failure modes and conditions of 24
asteroids with diameters less than 30 - 40 km, which were observed at high
resolution by ground radar or asteroid exploration missions. Assuming that the
material distribution is uniform, we investigate how these asteroids fail
structurally at different spin rates. Our FEM simulations describe the detailed
deformation mode of each irregularly shaped asteroid at fast spin. The failed
regions depend on the original shape. Spheroidal objects structurally fail from
the interior, while elongated objects experience structural failure on planes
perpendicular to the minimum moment of inertia axes in the middle of their
structure. Contact binary objects have structural failure across their most
sensitive cross sections. We further investigate if our FEM analysis is
consistent with earlier works that theoretically explored a uniformly rotating
triaxial ellipsoid. The results show that global shape variations may
significantly change the failure condition of an asteroid. Our work suggests
that it is critical to take into account the actual shapes of asteroids to
explore their failure modes in detail.
