Determination of the tensile constitutive relations of fiber reinforced concrete using inverse analysis

Abstract Fracture in fiber reinforced concrete involves the development of bridging stresses along the cracked faces, which is characterized in this work through a cracked hinge model. Closed-form solutions for the response have been developed using the analytical formulation for the three-point bending test of concrete considering a multi-linear stress-crack opening (σ-w) curve. A global optimization algorithm is used to determine the tensile constitutive relation represented by the σ-w curve, by identifying the parameters that provide the best fit with the load versus crack mouth opening displacement curve obtained. The ability of the model to give representative and unambiguous results has been assessed in terms of robustness and accuracy of fitting. The procedure has been applied for determining the tensile constitutive relations of steel and polymer fiber reinforced concrete with both softening and hardening-type behavior. The parameters thus obtained have been used to predict the response of different geometries of beams to assess the applicability of the methodology.