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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surfaces of the computational domains and they are able to capture accurately cracks propagation Ammendolea et al. (2021); Greco et al. (2021a), cracks coalescences phenomena, and multiple cracks initiation (Bruno and Greco (2001); Greco (2009); Greco et al. (2002); Pascuzzo et al. (2020)). The cohesive zone models (CZMs) are the most used discrete cohesive approaches for modeling the mechanical behavior of the fiber reinforced concrete materials (FRCs). They are based on different cohesive traction-separation laws that are appropriately defined to account for the effect of the reinforcing fibers incorporated in the concrete (Kazemi et al. (2007); Park et al. (2010)). To date, with reference to the ultra-high performance fiber reinforced concretes (UHPFRCs), the main efforts, from the numerical point of view, have been done for nano-enhanced UHPFRC elements without considering the additional reinforcing effect given by the steel rebars which is, instead, fundamental in the civil engineering field. Therefore, a numerical method able to simulate the fracture processes in UHPFRC beams reinforced with steel bars (at the macroscopic scale) and with nanoparticles (at the microscopic scale) is not still available in literature owing to the difficulties of incorporating all the different steel/concrete interactions which result to be strongly influenced by both micro- and nano-reinforcements. The present contribution is concerned with the cracking analysis in ultra-high performance fiber-reinforced concrete with embedded graphene nanoparticles and it is based on the coupling of two different numerical modeling approaches: the diffuse interface model (DIM) and the embedded truss model (ETM). The first model, introduced by some of the authors in De Maio et al. (2020c), considers the internal mesh boundaries of the computational domain as potential cracks which are modeled as cohesive elements whose mechanical behavior is described by a properly calibrated traction-separation law. The second model was already proposed in De Maio et al. (2019a), (2019b) for conventional RC structures and it was here adapted to simulate bond-slip behavior between steel and concrete which results influenced by the nano-reinforcements embedded in the UHPFRC mixture. Firstly, the theoretical background of the diffuse interface model and the embedded truss model is briefly recalled in Section 2. Then, in Section 3 the proposed fracture model has been firstly calibrated and, subsequently, it has been employed to simulate the cracking behavior of plain nano-enhanced UHPFRC beams and the obtained load displacement curves have been validated with comparisons based on experimental results. Finally, in Section 4 the proposed integrated numerical model has been employed to capture the mechanical behavior of steel bar-reinforced nano-enhanced UHPFRC beams. The numerical results highlight the strong influence which the embedded nano-reinforcement has on the crack width control, also demonstrating the strong capability of the proposed modeling strategy to predict the load-carrying capacity of UHPFRC structural elements reinforced at both the nano- and macro-scales. 2. Theoretical background In this section, the proposed computational framework based on the cohesive diffuse interface model (adopted for modeling the concrete) and the embedded truss model (adopted for modeling the bond-slip interface between concrete and steel rebars) has been briefly recalled giving additional details on the trilinear traction–separation law proposed for modeling nano-enhanced UHPFRC structures. 2.1. Diffuse interface approach for concrete modeling The diffuse interface model (DIM) has been recently proposed by some of the authors for plain and fiber reinforced concrete (FRC) respectively in De Maio et al. (2020b) and De Maio et al. (2020a). As can be seen in Figure 1, in this model a finite number of cohesive elements have been inserted between the bulk mesh elements (representing the concrete material) and their mechanical behavior has been defined through a nonlinear traction-separation law. This strategy can simulate multiple initiation and propagation of multiple cracks, crack branching and crack coalescence in quasi-brittle materials. Under the assumptions of small displacements, plane stress state, and absence of volumetric forces, the nonlinear equilibrium problem is written in a variational form and the discretized domain is composed by linear elastic planar volumetric elements and nonlinear four-node zero thickness interface elements (see De Maio et al. (2021), (2020d) for additional details). The mechanical behavior of the cohesive elements is given by an intrinsic traction separation law whose cohesive forces t acting along all the cohesive mesh boundaries can be defined in the following matrix form: