PSI - Issue 41

Andrea Pranno et al. / Procedia Structural Integrity 41 (2022) 618–630 Author name / Structural Integrity Procedia 00 (2019) 000–000

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(Acierno et al., 2017; Barretta et al., 2020, 2015; R. Barretta et al., 2018; Luciano, 2001). Additional damage phenomena associated with concrete materials can be caused by corrosion of the reinforcement steel, concrete cover separation and the debonding of the FRP system (De Maio et al., 2020b, 2019a). To examine the damage in reinforced concrete beams through parameters, such as damage location, damaged area, bending stiffness reduction, and damage evolution law, simplified models are available in the literature (Abdel Wahab et al., 1999). It is worth also noting that, the constraints conditions strongly effect the vibrational behavior of the reinforced concrete beams (simple (Cerri and Vestroni, 2000; Hanif et al., 2021; Koh et al., 2004a; Neild et al., 2002; Pešić et al., 2015; Voggu and Sasmal, 2021) or elastic (Casas and Aparicio, 1994) supports or free ends constraint (Van Den Abeele and De Visscher, 2000). As reported in the literature, several aspects of the mechanical behavior of reinforced concrete structures are highly dependent on the percentages of steel reinforcement, constraint conditions and geometry. For instance, in (Hamad et al., 2015) the numerical and experimental results performed on a reinforced concrete beam in a four-point bending test highlighted the natural vibration frequencies decrease as the level of damage increases reaching a maximum percentage reduction of about 16%. In (Casas and Aparicio, 1994) a simply supported reinforced concrete beams highlighted a natural vibration frequency reduction of about 25% and 15% for the first and the second vibration mode, respectively. Based on a numerical and experimental study by (Voggu and Sasmal, 2021), the first and fourth natural vibration frequencies were reduced by 55% and 29% due to the damage occurrence, respectively. Also in (Koh et al., 2004b) similar results have been obtained with a greater frequency reduction within 30% of the yielding load and with the fundamental vibration frequency reduced by 30% compared to the undamaged condition. The percentage decrease in natural vibration frequencies related to the maximum extent of the damage is about 40% in (Cerri and Vestroni, 2003) when the free ends constraint is introduced for the first mode shape, and about 33% and 24% for the second and fifth mode shapes respectively. In this study, using a cohesive fracture approach, a previous model presented by some of the authors (De Maio et al., 2020a) is extended to study the main factors influencing the static and dynamic response of reinforced concrete structures subjected to incremental static loading and unloading paths causing increasing levels of damage. Then, in order to investigate the degradation of vibration characteristics caused by the onset of cracking, a novel and advanced structural model is developed using the finite element method. Using interface elements, based on an advanced mixed-mode constitutive law, it is possible to account for both concrete plasticity, caused by cyclic tensile loading, and contact phenomena between crack surfaces. The contact phenomena induced by partial closure of the cracks caused by the presence of concrete aggregates were simulated using an adaptive formulation of the tangent stiffness at the point where the cohesive stresses change from tensile to compressive. A one-dimensional "truss" element is used to model and simulate the longitudinal and transverse steel reinforcement bars, and they are characterized by a purely axial mechanical behavior described by an elastoplastic constitutive law with linear hardening. One-dimensional "truss" elements are used to model the longitudinal and transverse steel reinforcement bars, and they are characterized by a purely axial elastoplastic mechanical behavior described by a constitutive law with linear hardening. Dynamical response is analyzed in terms of natural vibration frequencies and related modes shapes under quasi-static loading/unloading conditions of increasing amplitude, while the static mechanical response is analyzed in terms of load-displacement curves under monotonic and cyclic loading conditions. 2. Static and dynamic response of damaged structural systems under loading and unloading processes In the present work the degradation of vibration characteristics resulting from damage phenomena in reinforced concrete structures due to monotonic and cycling loading processes is investigated by using a numerical fracture model implemented in COMSOL Multiphysics® 5.6 finite element software. Two distinct mathematical models are incorporated: i) a diffuse interface model (DIM) that simulates the initiation and propagation of multiple cracks, and ii) an embedded truss model (ETM) to simulate the interaction between the concrete and steel reinforcements. The following works provide additional details on the study of the above-mentioned models (De Maio et al., 2020c, 2019b, 2022; Pascuzzo et al., 2022), whereas Section 2.1 describes the tensile concrete nonlinear cohesive law that was adopted to study the behavior of tensile concrete subjected to damage, plasticity, and contact phenomena. Additional details on the general formulation of the above-mentioned models can be found in the following works (De Maio et al., 2020c, 2019b, 2022, 2021), while the nonlinear cohesive law, adopted to simulate the mechanical behavior of concrete under tension subjected to damage, plasticity, and contact phenomena, is reported in the following section.