A First Approach to Comparing Cohesive Traction-Separation Laws for Concrete

In the already vast literature dealing with numerical simulations of fracture of concrete elements or structures, a large number of papers deal with cohesive traction-separation laws. However, in many instances, this appears to be a secondary aspect of the published studies, the principal one being the variant of the numerical algorithm being presented in the research. This makes difficult to compare the various available formulations for the vectorial traction-separation law (t–w law). The present work aims at initiating a systematic comparison between the t–w laws, and this is done comparing a subset of the possible formulations using exactly the same numerical algorithms. The analysis is restricted, in this contribution, to damage-based models in the tensile zone (positive normal components of the traction and the crack displacement vectors). All the models use the same uniaxial softening function and the emphasis is on the vectorial character of the t–w law, namely, on the influence of (1) the lack of coaxiality of t and w; (2) the shape of the damage criterion in the traction space; and (3) the influence of the ratio of fracture energies in pure modes I and II. The simulations have been carried out within the finite element framework COFE (Continuum Oriented Finite Element), which implements elements with an embedded adaptable crack to reproduce fracture of concrete as well as a smeared version that, essentially, unifies the numerical algorithms of both approaches.