PSI - Issue 41

Umberto De Maio et al. / Procedia Structural Integrity 41 (2022) 598–609 Author name / Structural Integrity Procedia 00 (2019) 000–000

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in adhesive-bonded ductile sheets ((Pascuzzo et al., 2020)), use various phenomenological-type traction-separation laws, depending on the simulated material, to describe the mechanical behavior of the cohesive forces acting along the crack faces, but suffer from mesh dependency issues partially solved by introducing moving mesh strategies ((Ammendolea et al., 2021; Greco et al., 2021a)). Diffuse interface models have been recently introduced to simulate the crack patterns of quasi-brittle materials and masonry structures, highlighting that a suitable calibration of the cohesive properties of the diffuse embedded interfaces is fundamental to ensure the desired numerical accuracy ((Skrame et al., 2022; Greco et al., 2022; Pascuzzo et al., 2022)). In the cracking analyses of RC structures, the concrete/rebar interaction modeling is fundamental to obtain correct predictions in terms of crack spacing and crack width. In this contest, the most used numerical fracture models employ interface elements and discrete bar elements, placed between concrete bulk elements and equipped with bond stress-slip relations to allow the propagation of any crack across the steel rebars avoiding undesired crack arrest effects ((Xu et al., 2017)). Moreover, has been numerically analyzed that the use of FRP plates bonded along the tensile faces of structural elements and the incorporation of nanomaterials in the concrete matrix improves the overall stiffness and the cracking behavior in RC structures as highlighted by some numerical results reported in ((De Maio et al., 2020a, 2022)). Interesting modeling strategies employed general adaptive multiscale and homogenization approaches to predict micro-cracking and contact evolution in composite materials ((Greco et al., 2018a, 2018b)) and to reduce the computational effort of the analysis. In this work, a numerical investigation of the cracking behavior, in terms of crack width and crack spacing, in RC structural elements, is performed by using an innovative integrated fracture model. This model, already employed by some of the authors in (De Maio et al., 2019a), adopts a cohesive zone approach and a bond-slip model to simulate the damage phenomena in the concrete phase and the mechanical interaction between steel rebars and surrounding concrete, respectively. Numerical simulations of RC specimens subjected to axial and shear/bending stress states have been performed and the obtained results are compared with experimental outcomes taken from the literature. The comparisons, in terms of loading curve, crack width and crack spacing, have demonstrated the capabilities and effectiveness of the proposed model to investigate the cracking behavior of RC structures. 2. The adopted numerical model for the RC structure analysis In this section, the numerical model employed to perform the cracking analysis is briefly described. Such a model can simulate the diffuse cracking behavior of reinforced concrete elements together with the interaction between concrete and steel rebars by virtue of a combined implementation of a diffuse interface model and an embedded truss model explained in Sections 2.1 and 2.2, respectively. 2.1. Diffuse interface model The diffuse interface model allows the crack initiation and propagation in the concrete phase to be suitable simulated by means of cohesive elements inserted between the bulk elements of a standard finite element mesh (Fig. 1a). The theoretical background of this model relies on a variational formulation written for a discretized domain consisting of linearly elastic planar volumetric elements and nonlinear cohesive interface elements, under the assumption of small displacements, plane stress state, and negligible inertial forces. In particular, the quasi-static equilibrium problem is formulated for a discretized body 2 h    subjected to body forces f in  and surface forces t on its Neumann boundary h N  , and containing multiple discontinuity lines h d  , which represent potential crack paths whose location is not a priori known. The associated BVP is expressed in the following weak form: find h h U  u such that:       \ \ d d d d h h h h h N d d d h h h h h h h h coh V                                  C u v t u v f v t v v (1) where C and ( )   are the fourth-order elasticity tensor and the linear strain operator, respectively, whereas h u and h v are the unknown displacement field and arbitrary virtual displacement field, respectively, which belong to the set of kinematically admissible displacements h U and to set of kinematically admissible variations of the approximated displacement field h V , respectively.