Vectorial stress-separation laws for cohesive cracking: in concrete and other quasibrittle materials

In the past 25 years, a considerable number of works on fracture of quasibrittle materials or structures has been published. A large fraction of such works makes use of cohesive crack models and, therefore, deals with cohesive traction–separation laws. However, in most instances, this appears to be a secondary aspect in the publications, the principal one being the variant of the numerical algorithm presented in the research. This makes it difficult to compare the various available formulations for the, necessarily vectorial, traction–separation laws ($$\mathbf{t}$$–$$\mathbf{w}$$ laws). The present work aims at initiating a systematic comparison between the $$\mathbf{t}$$–$$\mathbf{w}$$ laws, and this is done by comparing a subset of the possible formulations using exactly the same numerical algorithms. A damage-based model is presented which includes as particular cases most of the already published laws and which allows an independent specification of: (a) the softening function; (b) the lack of coaxiality of $$\mathbf{t}$$ and $$\mathbf{w}$$; (c) the shape of the fracture criterion in the traction space; and (d) the ratio of fracture energies in pure modes I and II. The performance of the models is numerically investigated for a simple, but crucial, case to reveal possible spurious influences of the foregoing issues (b)–(d).