  In this paper, we prove a compactness and semicontinuity result in $GSBD$ for
sequences with bounded Griffith energy. This generalises classical results in
$(G)SBV$ by Ambrosio and $SBD$ by Bellettini-Coscia-Dal Maso. As a result, the
static problem in Francfort-Marigo's variational approach to crack growth
admits (weak) solutions. Moreover, we obtain a compactness property for
minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have
recently shown the $\Gamma$-convergence to Griffith energy.
