PSI - Issue 39

Andrea Pranno et al. / Procedia Structural Integrity 39 (2022) 688–699 Author name / Structural Integrity Procedia 00 (2019) 000–000

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max w is the maximum displacement reached in the deformation history and

where t denotes the effective traction,

  max t w represents the trilinear traction separation law reported in Figure 2.

2.2. Embedded truss model for steel reinforcement modeling The embedded truss model is based on the concept of incorporate truss elements (representing the steel rebars) in the bidimensional domain (representing the concrete material). From the mechanical point of view, such truss elements are characterized by an elastoplastic constitutive behavior with a linear hardening able to describe the steel yielding stage. As shown in Figure 3a, the connection between the concrete and the truss elements is given by zero-thickness interface elements which are equipped by a bond-slip relation (reported in Figure 3b) which is taken from the CEB FIP Model Code Fib (2013) and it is strictly valid in the case of ribbed reinforcing bars and good bond conditions. It is worth noting that the displacement jump along the steel rebar direction is allowed while the displacement jump along the perpendicular direction to the steel rebar is assumed equal to zero. Thus, the only one active degree of freedom of the zero-thickness steel/concrete elements is the displacement jump along the rebar direction.

Fig. 3. Schematic representation of the connection between the concrete and the truss elements (a) and the bond-slip relation taken from CEB-FIP Model Code Fib (2013).

The bond stress–slip relation shown in Figure 3b is defined by the following parameters: ,max . b c f   3 9 , . mm s  1 0 1 , . mm s  2 0 6 , , ,max . b f b    0 4 and mm s  3 10 which coincides with the distance between ribs. In the normal direction is assumed a perfect bond between steel and concrete bond and thus the interfacial slip is the only one active degree of freedom. 3. Numerical results In this section, firstly the numerical outcomes involving plain nano-enhanced UHPFRC specimens were presented to calibrate the fracture parameters involving the cohesive interfaces, and comparisons with available experimental results have been reported to demonstrate the accuracy of the proposed numerical model. Subsequently, the structural response of the steel bar-reinforced UHPFRC beams reinforced with graphene nanoplatelets has been investigated in terms of the load-deflection curves and crack patterns.