Analytical solution of a gradient-enhanced damage model for quasi-brittle failure

This paper presents an approach for analytically solving gradient -enhanced damage (GED) models. The proposed approach provides rigorous proofs for essential phenomena observed in the traditional GED model, including damage widening, characteristic length sensitivity, and stress -locking. The derived cohesive law is a useful technique for accurately determining the material parameters of the GED model, significantly reducing the sensitivity to characteristic length. Furthermore, this study presents an isotropic damage model that considers both tensile and shear failures and can capture complex crack paths. Finally, a series of numerical examples is shown to demonstrate the efficacy of the suggested method.