Multi‐level approach for modelling the post‐cracking response of steel fibre reinforced concrete under monotonic and cyclic loading

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Abstract
In this contribution, a multi‐level Finite Element Model for steel‐fibre reinforced concrete (SFRC) is presented which allows predicting the post‐cracking response of fibre reinforced structural members. In contrast to the guidelines, which suggest that the response of SFRC should be derived indirectly, using bending tests, the post‐cracking response is here derived from the actual fibre properties. The numerical model is designed to directly track the influence of design parameters, such as fibre type, fibre orientation, fibre content and concrete strength, on the structural response. For this purpose, submodels on the level of a single fibre are combined into a crack bridging model, considering the fibre orientation and the fibre content. This is integrated into a finite element model for fiber reinforced concrete, in which a cohesive law in the context of the discrete crack approach is used to account for the opening of cracks [1]. The model has been extended to account for imperfect closure of cracks during cyclic loading and unloading, respectively, due to presence of fibres and debris within the crack, which is manifested in hysteresis loops in load‐displacement curves. The predictive capability of the proposed numerical multi‐level model for SFRC was systematically validated by means of test series performed on the fibre and the structural level [1,2]. The proposed model is validated by three‐point bending tests on notched beams with fibre content of 0 and 57 kg/m3 subjected to cyclic loading. The ability of the above‐described numerical model to capture the formation of hysteresis in cyclic loading is evaluated.

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