Effects of characteristic element length on fracture energy dissipation in continuum damage mechanics models

Progressive damage finite element (FE) analysis methods based on continuum damage mechanics (CDM) use mesh regularization algorithms to ensure that fracture energy dissipation predictions are independent of problem discretization. Mesh regularization algorithms require some geometric input related to the discretization. When using crack band theory for mesh regularization, a characteristic element length is used to approximate the width of the region affected by the continuum crack, i.e., the crack band width. Inaccuracy in representing the crack band width significantly affects predictions in terms of fracture energy dissipation. For square elements misaligned by 45°, using a typical line length across an element rather than the crack band width overestimates dissipated fracture energy by 41%. Not accounting for element aspect ratio underestimates dissipated fracture energy by 29% and 50% for ratios of two and four, respectively. Herein, methods for calculating characteristic element lengths in fiber-reinforced materials are presented that account for meshes being misaligned with respect to material directions, element aspect ratio, and element skew. The limits of applicability of different crack band width approximations are explored through numerical crack growth studies and center notch tension FE analyses for different discretizations. Results are compared in terms of fracture energy dissipation to linear elastic fracture mechanics. Analyses with the proposed characteristic element lengths predict consistent fracture energy dissipation with various meshes. The proposed methods and the included studies on potential error in fracture energy dissipation provide analysts the basis to better understand error in CDM model predictions associated with simplified FE model preprocessing.