Crack Models for Concrete, Discrete or Smeared? Fixed, Multi-Directional or Rotating?

Numerical tools to simulate cracking in concrete and similar materials are developed. Firstly, a treatment is given of smeared and discrete crack concepts, which start from the notion of a continuum and a discontinuum respectively. With the smeared crack concept a distinction is furthermore made between fixed, multi-directional and rotating cracks, whereby the orientation of the crack is kept constant, updated in a stepwise manner or updated continuously respectively. Secondly, descriptions of the material behavior at cracking and fracture are presented. Key-effects herein are the tensile-softening behaviour normal to the crack (mode I) and the shear retention parallel to the crack (mode II). Thirdly, the resulting models are applied to scrutinize localized fracture in concrete. Attention is given to tension-shear problems whereby the principal stresses rotate after crack initiation, as is typical of general crack analysis. The results for the various crack concepts show large discrepancies. Smeared cracks may give rise to stress-locking while discrete cracks do not. Fixed smeared cracks may produce overstiff behavior while rotating smeared cracks do not.Civil Engineering and Geoscience