Some recent results on the convergence of damage to fracture

Abstract

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.