Some recent results on the convergence of damage to fracture

We discuss a recent approximation result for Barenblatt's cohesive fracture energies in the case of antiplane shear. The regularized functionals are damage energies of Ambrosio--Tortorelli type and the approximation is obtained in the sense of $\Gamma$-convergence. The extension to the general case of linearized elasticity in dimension $n$ is still an open problem. To prepare for this extension we study the structure of a subclass of functions of bounded deformation.