An orthotropic material model for steel fibre reinforced concrete based on the orientation distribution of fibres

In the present paper the authors focus on constitutive mappings for steel fibre reinforced concrete, SFRC. The anisotropic properties of this composite are caused by the orientation distribution of fibres. The constitutive relation is developed for one meso-volume element of SFRC as a combination of isotropic and orthotropic St. Venant–Kirchhoff material models, which are applied to concrete matrix and to steel fibres, respectively. The alignment tensors and orientation distribution function adopted from the mesoscopic continuum theory are utilised to identify the material meso-symmetry axes and to asses the contribution of fibres in the symmetry axes defined. While assessing the orthotropic meso-elasticity for fibres, the elasticity of an individual fibre in its local coordinates is transformed into the material meso-symmetry axes and weighted with the orientation distribution function of fibres. The advantage of the material model developed for SFRC is that it uses complete orientation information of fibres (two angles in spherical coordinates) and utilises tensor quantities complying with material objectivity.