Issue 68

U. De Maio et alii, Frattura ed Integrità Strutturale, 68 (2024) 422-439; DOI: 10.3221/IGF-ESIS.68.28

of structural deterioration and highlights the importance of comprehensive assessment methods in ensuring the reliability and safety of the material under consideration.

Undamaged – L1’ 1.0000 0.3658 0.1074 0.0137 0.0026 0.3658 1.0000 0.2882 0.0014 0.0009 0.1074 0.2882 1.0000 0.0815 0.0003 0.0137 0.0014 0.0815 1.0000 0.8299 0.0026 0.0009 0.0003 0.8299 1.0000 Undamaged – L2’ 1.0000 0.3926 0.1089 0.0144 0.0024 0.3711 1.0000 0.2880 0.0020 0.0007 0.1040 0.2635 0.9997 0.0871 0.0001 0.0139 0.0012 0.0749 0.9998 0.8419 0.0023 0.0006 0.0007 0.8272 0.9997 Undamaged – L3’ 0.9997 0.3602 0.1177 0.0585 0.0019 0.3533 0.9994 0.2781 0.0004 0.0001 0.1145 0.2913 0.9962 0.1078 0.0004 0.0148 0.0015 0.0585 0.9583 0.8715 0.0021 0.0007 0.0031 0.8199 0.9958

Undamaged – L4’ 0.9997 0.2021 0.1538 0.1582 0.0016 0.3501 0.9645 0.2308 0.0234 0.0000 0.1172 0.4610 0.9895 0.1187 0.0013 0.0139 0.0036 0.0578 0.8214 0.8821 0.0028 0.0033 0.0036 0.6296 0.9929 Undamaged – L5’ 0.9998 0.2444 0.1303 0.2220 0.0015 0.3520 0.9811 0.2597 0.0112 0.0000 0.1159 0.4121 0.9952 0.2388 0.0010 0.0141 0.0027 0.0613 0.7332 0.8739 0.0026 0.0027 0.0028 0.4332 0.9949

Undamaged – L6’ 0.9997 0.2405 0.1307 0.4954 0.0012 0.3495 0.9792 0.2589 0.0506 0.0000 0.1174 0.4151 0.9944 0.3144 0.0018 0.0144 0.0022 0.0601 0.2252 0.8802 0.0025 0.0033 0.0030 0.0458 0.9933 Table 6: Modal Assurance Criterion (MAC) for the investigated damage levels with respect to the undamaged configurations for the non-symmetric three-point bending test. Additionally, the curves associated with the higher vibration modes present increasingly complex oscillatory trends; such behavior is most emphasized for the fifth vibration mode shape (see Fig. 9). As a matter of fact, as the level of damage increases, beyond the peak point at which the coalescence of different micro-cracks into a single macro-crack occurs, the curves deviate more and more from that representing the undeformed condition. It is important to remind, however, that the undamaged condition and the condition associated with the L1’ level, represented by the orange and black lines in Fig. 9 respectively, are completely overlapping since, as can be seen from the displacement-load curve (Fig. 7), the first unloading path has been carried out for a displacement value that is still associated to a linear-elastic behavior. n the present work, an improved numerical model to investigate the crack-induced degradation of the vibration characteristics in plain concrete structures has been presented. In particular, proper traction-separation laws adapted for cycling loading conditions including frictional effects, have been developed in order to capture the complex non linear phenomena induced by the load application, such as such as concrete plasticity, partial closure of the cracks, and aggregate interlocking. The proposed numerical method has been employed for two different numerical applications, a symmetric and a non-symmetric three-point bending test in order to analyze the structural behavior under mode-I and mixed-mode fracture conditions, respectively. I C ONCLUSIONS

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