Phase-field regularized cohesive zone model (CZM) and size effect of concrete

A phase-field regularized cohesive zone model (CZM) was recently proposed for both brittle fracture and cohesive failure within the framework of the unified phase-field damage theory. Motivated from the fact that this model gives length scale and mesh independent global responses for problems with or without elastic singularities, we further apply it in this work against the size and boundary effects of concrete under both mode-I and mixed-mode failure. More specifically, for the two independent experimental campaigns of three-point bending notched and unnotched concrete beams under mode-I failure, the quality of data-fitting is, at least, comparable to the best results reported in the literature. For another series of eccentrically notched concrete beam tests, the size effect with transition from mode-I fracture to mixed-mode failure is also predicted. In all numerical examples, not only the peak loads but also the softening regimes agree well with the experimental results using a single set of material parameters for a specific series of tests. Being accompanied with other merits, e.g., generic softening laws, no lateral widening, no need of extrinsic crack tracking nor the penalty stiffness, etc., the presented phase-field regularized CZM can be used as a promising approach in the modeling of damage and failure in solids and structures.