Cohesive crack models for semi-brittle materials derived from localization of damage coupled to plasticity

Abstract

Based on discontinuous displacement approximation of the continuum and ‘shear band’ kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a ‘fixed crack’ model is obtained. A ‘discrete crack’ strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.