PSI - Issue 47

Luciano Feo et al. / Procedia Structural Integrity 47 (2023) 800–811 Author name / Structural Integrity Procedia 00 (2019) 000–000

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(a) (b) Figure 10 . (a) Correlation between nanofiller content (%) and elastic bond stress �� (MPa); (b) Correlation between nanofiller content (%) and residual bond stress � (MPa). 4. Conclusions The purpose of this work was to enhance the meso-mechanical formulation of the well ‐ known non ‐ linear cracked ‐ hinge model, initially formulated by Martinelli et al. (2020) and then extended for the case of High ‐ Performance Concrete with steel fibers under freeze and thaw cycles by Martinelli et al. (2021) and Penna et al. (2022). The novel formulation of the model is able to predict the bending behavior of UHPFRC with nanofiller. In particular, a back analysis has been developed to calibrate the stress-strain parameters of the cementitious matrix and those of the bond slip laws for steel fibers by using the experimental results already available in the literature. On the basis of the aforementioned back-analysis, the following conclusion can be noted:  by carefully modifying the fracture energy parameters (i.e., , �� and ��� � related to the stress-strain behavior of the cement matrix it is possible to take into account the bridging effect of nanofillers;  the presence of nanofillers results in a softening behavior of the second branch of the trilinear bond-slip law;  for each mixture, a quasi-linear correlation between the nanofiller content and the fracture energy parameters of cement matrix is exhibited, as well as between the nanofiller content and bond stresses of fibers. These numerical results show a good agreement between the experimental data and the values obtained from the modified model. In conclusion, the preliminary results presented in this paper demonstrate that the model is able to predict the post cracking behavior of UHPFRC with nanofiller. However, further experimental results are needed to calibrate general relationships between the main parameters that control the bond-slip law of fibers and the stress-strain relation in presence of nanofillers: this aspect will be examined in future developments of the present research. Acknowledgements The authors gratefully acknowledge the financial support of the Italian Ministry of University and Research (MUR), Research Grant PRIN 2020 No. 2020EBLPLS on “ Opportunities and challenges of nanotechnology in advanced and green construction materials ”. References ASTM C 109. Standard test method for compressive strength of hydraulic cement mortars (using 2-in. or [50-mm] cube specimens). West Conshohocken: ASTM International; 1999. ASTM C 1609. Standard test method for flexural performance of fiber reinforced concrete (using beam with third-point loading). West Conshohocken: ASTM International; 2005. Beghini, A. et al. (2007). Microplane model M5f for multiaxial behavior and fracture of fiber-reinforced concrete. Journal of Engineering Mechanics 133, 66–75. Caggiano, A et al. (2012). Zero-thickness interface model formulation for failure behavior of fiber-reinforced cementitious composites. Computation Structures 98, 23–32.