Numerical modelling of the pull-out response of inclined hooked steel fibres

Steel fibre reinforced concrete (SFRC) is an anisotropic material due to the random orientation of the fibres within the cement matrix. Fibres under different inclination angles provide different strength contribution of a given crack width. For that the pull-out response of inclined fibres is of great importance to understand SFRC behaviour, particularly in the case of fibres with hooked ends, which are the most widely used. The paper focuses on the numerical modelling of the pull-out response of this kind of fibres from high-strength cementitious matrix in order to study the effects of different inclination angles of the fibres to the load-displacement pull-out curves. The pull-out of the fibres is studied by means of accurate three-dimensional finite element models, which take into account the nonlinearities that are present in the physical model, such as the nonlinear bonding between the fibre and the matrix in the early stages of the loading, the unilateral contact between the fibre and the matrix, the friction at the contact areas, the plastification of the steel fibre and the plastification and cracking of the cementitious matrix. The bonding properties of the fibre-matrix interface considered in the numerical model are based on experimental results of pull-out tests on straight fibres.