Anisotropic gradient-enhanced eikonal non-local damage modeling of quasi-brittle materials

Continuum damage models are widely used to simulate cracking in quasi-brittle materials like concrete, masonry, and certain rocks. However, these models produce mesh-sensitive results in structural simulations unless properly regularized. Conventional regularization strategies often suffer from notable shortcomings. To address these issues, non-local models featuring evolving non-local interactions have been developed. Among them, the eikonal non-local approach introduces evolving non-local interactions by considering that the interaction distance between two material points is their geodesic distance in a Riemannian space deformed by damage. Accordingly, a metric field, derived in a differential geometry context, fully characterizes this deformation. This contribution presents a gradient-enhanced eikonal non-local formulation coupled with a second-order anisotropic damage model. Such a combination is particularly relevant for quasi-brittle materials, whose behavior is directionally dependent and exhibits features like tension–compression asymmetry and unilateral effects. The paper provides an overview of the theoretical formulation, numerical implementation, and test cases, with particular emphasis on the regularization capabilities and the ability to capture the progressive tendency toward a transition from diffuse damage to localized fracture.