Some recent developments in FE-modelling of cracking in concrete and quasi-brittle materials

The development of numerical models able to simulate the complex physical behaviour of concrete cracking is a very peculiar subject, as an "exhaustive" model that performs in every condition does not so far exist. In this contribution, the specific finite element formulations of two distinct three-dimensional continuum models are presented: an isotropic scalar damage model (SDM) and a rotating crack model (RCM). According to the isotropic SDM model, the loss of integrity of the material is controlled by a single scalar parameter. The resulting damaged stiffness tensor is a scalar multiple of the elastic stiffness tensor, so it decreases proportionally in every direction, independently of the direction of the loading. On the other hand, the RCM reproduces the anisotropic behaviour of cracking. The implemented version allows the formation of up to three mutually orthogonal cracks, which keep, aligned with the principal directions (of both stresses and strains). For both the above models, some implementation devices and numerical algorithms (also useful for other constitutive laws) are described. The models are implemented into an 8-node isoparametric volume element and tested in the analysis of simple but representative structures, for which experimental tests and different numerical simulations are available.