Phase field and gradient enhanced damage models for quasi-brittle failure: A numerical comparative study

•Phase-field regularized CZM and GED models for cohesive fracture are compared.•PF-CZM converges to a discrete CZM, is mesh and length scale independent.•GED is mesh independent but length scale dependent. It suffers from damage widening.•Stress based GED removed drawbacks of GED but is not completely mesh insensitive.•PFM has an exponential crack like damage distribution whereas GED yields a bell like damage profile.•PF-CZM is more computationally intensive than GED/SB-GED. This paper presents a comparative study of the gradient-enhanced damage models (GED) of Peerlings et al. (1996), Vandoren and Simone (2018) and the phase field damage/fracture model (PFM) of Wu (2017), Wu and Nguyen (2018) within the context of the computational modeling of the fracture of quasi-brittle materials (concrete, ceramic, rock, ice, etc.). Being continuous damage/fracture models, these two models enjoy the simplicity of modeling the fracture process on a fixed finite element mesh. The similarities and differences of the two models are discussed by examining governing equations and conducting numerical simulations of some mode I and mixed-mode fracture benchmark tests. The most worthy findings are: (i) both classes of models can handle the initiation and propagation of cohesive cracks, (ii) they are totally different–PFM behaves like a cohesive zone model (a sub-class of fracture mechanics) when the length scale is sufficiently small and the response is insensitive to this length scale whereas GED is a non-local damage model (a sub-class of continuum damage mechanics) of which response obviously depends on the length scale.