  The failure of brittle solids involves, before macroscopic rupture, power-law
distributed avalanches of local rupture events whereby microcracks nucleate and
grow, which are also observed in for an elastic interface evolving in a
non-homogeneous medium. For this reason, it is tempting to relate failure to
the depinning of an elastic interface. Here we compute the elastic kernel of
the interface representing the damage field of a brittle solid. In the case of
a damage model of rupture under compression, which implements the Mohr-Coulomb
criterion at the local scale, we show that the elastic kernel is unstable, and
hence is very different from the kernels of usual interfaces. We show that the
unstable modes are responsible for the localization of damage along a
macroscopic fault observed in numerical simulations. At low disorder, the most
unstable mode gives the orientation of the macroscopic fault that we measure in
numerical simulations. The orientation of the fault changes when the level of
disorder is increased, suggesting a complex interplay of the unstable modes and
the disorder.
