  We introduce a lattice model able to describe damage and yielding in
heterogeneous materials ranging from brittle to ductile ones. Ductile fracture
surfaces, obtained when the system breaks once the strain is completely
localized, are shown to correspond to minimum energy surfaces. The similarity
of the resulting fracture paths to the limits of brittle fracture or minimum
energy surfaces is quantified. The model exhibits a smooth transition from
brittleness to ductility. The dynamics of yielding exhibits avalanches with a
power-law distribution.
