Sharp-interface limits for brittle fracture via the inverse-deformation formulation

We derive sharp -interface models for one-dimensional brittle fracture via the inverse -deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non -convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse -strain gradient. They predict spontaneous fracture with exact crack -opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces in the Gamma-limit. Accordingly, we construct energyminimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.