A derivation of Griffith functionals from discrete finite-difference models
We analyze a finite-difference approximation of a functional of Ambrosio–Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step δ is smaller than the ellipticity parameter ε, we show the Γ-convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no Lp fidelity term.