Mesh objectivity in dynamic fracture analyses with rate dependent continuum damage models

Abstract

This paper is aimed at investigating the mesh objectivity in dynamic fracture analyses employing strain rate dependent damage evolution as the localization limiter. Specifically, the goal is investigating and understanding the limits of applicability across various loading rates. For this purpose, dynamic fracture of a brittle material is simulated using a rate dependent scalar damage model. Dynamic fracture scenarios under a wide range of loading rates are considered, which yield various fracturing patterns ranging from localized to branched/diffused. The rate dependent damage model is seen to yield mesh objective predictions only at higher loading rates, which correspond to branched/diffused fractures. Results are not mesh objective at lower loading rates, which correspond to localized fractures. The regularization effect, at higher rates, is due to an intrinsic length-scale induced by the rate dependent damage law, and is related to the strain rate sensitivity parameter. For these cases, the predicted fracture patterns consist of thickened damage bands, spanning multiple element widths, and are wider than the intrinsic length-scale induced by the model. Thus, this feature can be viewed as a physical manifestation of the intrinsic length-scale. Wave propagation and dispersion in a one-dimensional version of the present damage model is analyzed further to explain the results. It is demonstrated that the group and phase velocity are finite and approach the elastic wave speed at higher loading rates, helping retain mesh objectivity. However they approach infinity at lower loading rates, causing the regularizing effect to vanish. Thus, the rate dependent damage model does not yield mesh objective results across all loading rates, and must be employed with caution.