LOCALIZATION ANALYSIS OF NONLOCAL MODEL-BASED ON CRACK INTERACTIONS

The conventional nonlocal model, often used as a localization limiter for continuum-based constitutive laws with Strain-softening, has been based on an isotropic averaging function. It has recently been shown t hat this type of nonlocal averaging leads to a model that cannot satis factorily reproduce experimental results for very different test geome trics without modifying the value of the characteristic length dependi ng on geometry. A micromechanically based enrichment of the nonlocal o perator by a term taking into account the directional dependence of cr ack interactions can be expected to improve the performance of the non local model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one-dimension al description. Strain localization in an infinite layer under plane s tress is studied using both the old and the new nonlocal formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between th e localization sensitivity of the old and new model are pointed out. I n addition to the detection of bifurcations from an initially uniform state, the stable branch of the load-displacement diagram is followed using an incremental procedure.