PSI - Issue 47

Francesco Ascione et al. / Procedia Structural Integrity 47 (2023) 460–468 Author name / Structural Integrity Procedia 00 (2019) 000–000

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discontinuity inserted in the material domain by duplicating nodes of a standard finite element mesh (Xu and Needleman, 1994; Campilho et al., 2013). Such models are also employed together with moving mesh techniques in order to reduce the directional mesh-bias dependency issues induced by the crack propagation in mixed-mode fracture conditions, as reported in some works (Ammendolea et al., 2021; Greco et al., 2021; Pascuzzo et al., 2022). On the other hand, smeared fracture models simulate the damage processes as a progressive loss of the material integrity through constitutive relations in which the mechanical effect of the crack growth is introduced with internal state variables which act on the degradation of the material elastic stiffness involving strain-softening laws to describe the post-peak gradual decline of stress at increasing strain, see for instance (Cervera and Chiumenti, 2006). In this work, based on the numerical procedure already proposed by some of the authors (De Maio et al., 2023a), the global structural response, in terms of load-carrying capacity and failure modes, of plain and reinforced concrete beams retrofitted with FRP sheets bonded to the concrete surface by nano-enhanced epoxy resin, has been numerically investigated. Comparisons between the results obtained by the simulations and experimental tests, available in the technical literature, have highlighted the effectiveness of the proposed model in simulating the mechanical behavior of the investigated RC structures and the beneficial effects of the nano-enhanced epoxy on the concrete-FRP bond strength. 2. Description of the numerical model for nano-enhanced FRP-plated RC elements In this section, the integrated model adopted to analyze nano-enhanced FRP-plated RC elements is briefly described. In particular, the concrete and FRP system modeling, based on a cohesive fracture approach, is explained in Section 2.1, while the steel reinforcement, which relies on an embedded truss model, is illustrated in Section 2.2. 2.1. Cohesive approach for concrete and nano-enhanced FRP system modeling The damage phenomena occurring in nano-enhanced FRP-plated RC elements have been simulated by using a cohesive zone model. In particular, a diffuse crack approach, already proposed by some of the authors (Pranno et al., 2022b; Gaetano et al., 2022), is adopted to simulate crack onset and propagation in the concrete phase. It is based on cohesive elements, placed between the finite elements of the adopted computational discretization, able to describe the nonlinear process through a suitable traction-separation law. On the other hand, debonding phenomena, occurring along the physical interface between the concrete and the FRP system, are simulated by adopting a single crack model, according to which zero-thickness cohesive elements, equipped with a specific bond-slip law, simulate the bond behavior between the FRP plate and concrete. Fig. 1 illustrates a schematic representation of the proposed model.

f t t n

δ 0

δ n

τ τ max

Concrete bulk element

FRP bulk element

Concrete/FRP cohesive elements Concrete cohesive elements Crack

δ 1

δ 2

δ f

δ s

Fig. 1. Schematic representation of the proposed model and adopted cohesive laws.