Orthotropic elastic properties for UHPFRC based on two-phase model homogenization

Ultra-high-performance fiber reinforced concrete (UHPFRC) is a durable composite with ductile behavior. It has been investigated for application on structures submitted to complex stress states as bridges and wind towers (onshore and off-shore). During casting and compaction, fiber alignment may occur so that UHPFRC has a mechanical response that is dependent on the direction of loading. Consequently, orthotropic elastic properties are necessary for any stress-strain analysis to take these effects into account. Although experimental analysis is always welcome to evaluate the elastic properties of materials, significant challenges would appear to evaluate the orthotropic response experimentally. On the other hand, three-dimensional finite element models may be used to incorporate short fibers individually (one by one) into the model to gain sensitivity to their influence in accordance with orientation patterns that may occur in real situations. Within the elastic regime, this type of simulation is not computationally costly and may be developed in standard personal computers. Therefore, the present study applies numerical homogenization to propose equations for estimating the orthotropic properties of UHPFRC. Fibers are generated covering all orientations (0< eta theta <1). Relations between fiber efficiency and eta theta are established to determine the orthotropic matrix based on the phase properties (matrix and fibers) and fiber content.