Nonlocal Model Based on Crack Interactions: A Localization Study

A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions (Bazˇant, 1992) can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one-dimensional description. Strain localization in an infinite layer under plain stress is studied using both the old and the new nonlocal formulations. The importance of renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out.