Continuous microplane theory and interface approach for failure form analysis of steel fiber reinforced concrete

A fracture energy-based microplane constitutive theory for steel fiber reinforced concrete (SFRC) is presented to evaluate the properties of the discontinuous bifurcation condition under different scenarios of stress states, fiber contents and directions. The constitutive model considers a CAP-cone yield surface of C1 continuity at the microplane level. Its evolution in the post-peak regime is described by means of a fracture energy-based work softening which is defined differently for mode I and II type of failure. The effect on the post-peak ductility introduced by the fiber content is also taken into account, while the directional properties of the steel fibers are considered through the relative directions between microplanes and fibers. The main objective of the discontinuous bifurcation analysis proposed in this work, is to evaluate the capabilities of the microplane theory to capture the directional enrichment provided by steel fibers to the ductility and also, to reproduce the particular microcrack directions which (in the framework of the smeared crack approach) are mathematically represented by the spectral properties of the critical localization tensor. Firstly, the localized failure features in the form of discontinuous bifurcation of SFRC are identified by means of numerical analysis. Mono- and multidirectional fiber distributions and different steel fiber contents are considered in the localized failure analysis to be performed on stress states corresponding to critical strengths of SFRC under both uniaxial and biaxial tension and compression. Then, microplane model are compared with the FE predictions obtained with the interface model for FRC previously proposed by the authors. In the last case, the crack evolutions and their directions are explicitly described throughout the so-called discrete crack approach