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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I c G , II c G denote the normal/tangential critical interface stresses and the critical mode I/II

where the c  , c  and

fracture energies, respectively. 2.2. Embedded truss model

The steel reinforcing system, including stirrups and rebars, embedded in the concrete structure is modeled by two node discrete truss elements and connected to the concrete phase by zero-thickness interfaces elements equipped with a bond stress-slip relation taken from ((C.E.-I du B. (CEB-FIP), 2013)) and depicted in Fig. 2a, able to describe the mechanical behavior of the tangential forces between steel and surrounding concrete. Moreover, the material response of reinforcing steel bars is elastoplastic with linear hardening. Such embedded 1D truss elements (see Fig. 2b), in which all the individual steel rebars and stirrups at a given depth are concentrated, have an equivalent section assigned as the sum of the cross-sections of individual steel elements (rebars and stirrups legs, respectively. The truss elements are constrained in the perpendicular direction to the rebar meaning that only the displacement jump in the rebar direction (i.e. the slip) is considered an active degree of freedom of the zero-thickness steel/concrete interface element. Along the steel rebars and stirrups, no cohesive elements have been inserted at the inter-element boundaries superposed to the existing truss elements. Moreover, the material response of reinforcing steel bars is elastoplastic with linear hardening.

Fig. 2. (a) Adopted bond-slip relation taken from (C.E.-I du B. (CEB-FIP), 2013); (b) schematic representation of the embedded truss model.

3. Cracking analysis of RC structural elements In this Section, the proposed integrated model has been employed to simulate the load-carrying capacity and the related crack patterns of RC members subjected to general loading conditions. The cracking behavior has been in depth analyzed by computing crack width and crack spacing. Comparisons with available experimental and numerical results are reported. 3.1. RC member subjected to axial loading conditions The first numerically tested specimen is an axially loaded RC structural element experimentally investigated by (Lee and Kim, 2009) whose geometric configuration and boundary conditions are depicted in Fig. 3a. The concrete domain of the RC members has been discretized by performing a Delaunay tessellation, consisting of planar three node bulk elements with a prescribed maximum edge length of 30 mm, enriched by four-node zero-thickness interface elements placed along the boundaries of the considered mesh (see Fig. 3b), while, two-node truss elements are employed to model the steel rebars.