PSI - Issue 47

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

461

2

Keywords: Nano-modified epoxy resin; nanomaterials; strengthened structures; cohesive zone model; finite element modeling.

Nomenclature ( ) f δ

softening function

maximum effective displacement jump

δ

normal and tangential components of the displacement jump

, n s δ δ

critical displacement

0 δ

Young’s modulus of the bulk

E

fracture energy

f G

critical tensile strength

t f

mesh size

mesh L , n s t t

normal and tangential components of the cohesive traction vector

Poisson’s ratio of the bulk

ν

  δ

displacement jump between the crack faces

1. Introduction The recent progress in nanotechnology research has motivated many researchers to employ nanomaterials in the building engineering field in order to improve the mechanical properties of concrete and composite materials (Casati and Vedani, 2014; Chuah et al., 2014; Chwał and Muc, 2019) . As a matter of fact, innovative materials (i.e. nano- and micro-reinforced composites proposed in (De Maio et al., 2020a, 2020b) and advanced bio-inspired metamaterials for elastic wave attenuation (Yin et al., 2021; Pranno et al., 2022a; De Maio et al., 2023b)) are becoming the most common choice to retrofit existing structures. However, several experiments highlighted that only specific amounts of nano materials incorporated in the concrete matrix improve the compressive and tensile strength of these structures (Li et al., 2013; Meng and Khayat, 2016). In fact, in samples containing more than 0.1 wt% of CNT, a sharp decrease in both tensile and compressive strength, due to the formation of weak regions induced by the agglomeration of CNT, is clearly detected, see for instance (Qasem et al., 2020; Ammendolea et al., 2023). Moreover, nanoscale reinforcements have been also embedded in composite materials to improve the bond strength between concrete and FRP plate in retrofitted reinforced concrete structures (Diab and Farghal, 2014; Kononova et al., 2016; Wang et al., 2021; Wernik and Meguid, 2014). Experimental results show benefic effects of such nano-modified composite in terms of bond stress and crack patterns (Irshidat and Al-Saleh, 2016). The incorporation of nanofillers in epoxy resin, useful to bond the FRP sheets to each other and along the concrete surface, leads to an improvement of the mechanical performance of the FRP concrete bond, thus enhancing the overall effectiveness of the strengthening structural system ((Hu et al., 2012)). (Li et al., 2017; Rousakis et al., 2014) highlighted that the addition of nano-silica powder in the epoxy binder greatly improves its workability, ductility, and strength and that enhanced bonding between FRP and concrete can be achieved by employing a nano-modified FRP glue. (Irshidat et al., 2016) investigated the effect of carbon nanotube addition in epoxy resin adhesive in retro-fitted beams highlighting an increase of both stiffness and ultimate load with an improvement of the mechanical performance strongly related to the percentage of nanofiller dispersion. With respect to the high number of experimental works about nano-modified concrete structures, there are few numerical models able to take into account the presence of nano-reinforcement in cement matrix or composite materials. In general, such kinds of structures should be analyzed by multiscale models (Greco et al., 2020) in order to simulate the different mechanical behaviors which arise at the nano and micro scale, such as crack bridging offered by the CNT, and debonding phenomena between mortar and aggregates (Bruno et al., 2009; Greco, 2009). However, due to the great computational effort required by the multiscale models, macro-scale models, based on phenomenological-type approaches, are preferred (Ascione et al., 2019; Ascione and Mancusi, 2010). In particular, discrete and smeared damage models can be employed to analyze nano-modified concrete structures. Within the discrete model group, we can find the cohesive zone models, according to which the crack arises as a geometric