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. • This paper introduces a mathematical approach for the analytical solution of gradient-enhanced damage (GED) models. • The analytic solution alleviates the characteristic length sensitivity in the GED model. • The proposed damage evolution method can effectively capture complex crack paths. [ABSTRACT FROM AUTHOR]