A localizing gradient damage enhancement with micromorphic stress‐based anisotropic nonlocal interactions

Summary This article presents a localizing gradient damage model with evolving micromorphic stress‐based anisotropic nonlocal interactions. The objective is to model mesh independent fracture behavior of quasi‐brittle materials, and to avoid the issues associated with the existing gradient‐enhanced damage models. In the proposed model, an evolving anisotropic nonlocal interaction domain governs the spatial diffusive behavior, which helps to maintain a localized damage bandwidth during the final stages of loading. The anisotropy in nonlocal interactions is captured through an anisotropic gradient tensor, which defines the orientation of the diffusive interaction domain based on the principal stresses at a given material point. In this article, a smooth micromorphic stress tensor is utilized for the determination of principal stress states, to enforce a properly oriented interaction across the bandwidth of the damage process zone throughout the loading process. The proposed approach also enables the usage of low order finite elements without any oscillatory micromorphic or nonlocal equivalent strain response in the later stages of deformation. The accuracy and performance of the proposed model are demonstrated numerically in plane strain/stress for mode‐I, mode‐II, and mixed‐mode loading conditions.