  We explore corrections in the blackfold approach, which is a worldvolume
theory capturing the dynamics of thin black branes. The corrections probe the
fine structure of the branes, going beyond the approximation in which they are
infinitely thin, and account for the dipole moment of worldvolume stress-energy
as well as the internal spin degrees of freedom. We show that the dipole
correction is induced elastically by bending a black brane. We argue that the
long-wavelength linear response coefficient capturing this effect is a
relativistic generalization of the Young modulus of elastic materials and we
compute it analytically. Using this we draw predictions for black rings in
dimensions greater than six. Furthermore, we employ our corrected blackfold
equations to various multi-spinning black hole configurations in the blackfold
limit, finding perfect agreement with known analytic solutions.
