Strain localization, strong discontinuities and material fracture: matches and mismatches

The work focuses on the connections of strain localization modeling of material failure and discrete fracture mechanics. It is an attempt to give an answer to the old question of whether the finite element solutions of material failure problems based on strain localization techniques, using standard continuum stress–strain constitutive models equipped with strain softening, have physical sense as solutions of de-cohesive fracture mechanics problems. Based on some well-established links of the Continuum Strong Discontinuity Approach (CSDA) to material failure and cohesive fracture mechanics, some objective indicators are proposed to assess the quality of strain localization results. These indicators are simply derived on the basis of the inelastic strain distribution provided by the strain localization solutions and the direction of propagation of the localization band. They can be computed without knowledge of the exact fracture mechanics solution of the problem, and used as error indicators in a large variety of material failure situations. The proposed indicators are assessed, by means of their application to evaluation of a number of strain localization solutions of benchmark problems. Issues as the influence of the mesh structure and alignment, type of constitutive model and considered finite element techniques are examined. On the light of the obtained results, classical flaws in strain localization solutions, as mesh bias dependence and stress-locking are reinterpreted.