PSI - Issue 37

Khalil Naciri et al. / Procedia Structural Integrity 37 (2022) 469–476 Khalil Naciri et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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material, denoted [Σ] and [E] respectively, are derived from t he RVE stress and strain tensors using the following equations (Pegon and Anthoine, 1997): [Σ] = 1 ∫ [σ] () [E] = 1 ∫ [ε] () Where S is the area of the RVE. Various RVE geometrical shapes have been adopted in the literature. In this work, the tested arch periodicity oriented the choice of the RVE to the shape shown in Fig. 3. To determine the strength capacity and the post-elastic behavior of the homogenized masonry in compression and tension, the RVE was subjected to a vertical uniaxial compressive and tensile strains. Furthermore, a biaxial compressive strain test was conducted to derive the 0 / 0 parameter. Input parameters governing the behavior of brick, mortar, and interfaces constituting the RVE were kept as in Section 4.1. Numerical stress-strain curves are shown in Fig. 4. Concerning the elastic behavior, the bending applied to the arch is initially transformed into compression , therefore Young’s modulus was determined as the slope of the linear part of the uniaxial compressive stress-strain curve plotted in Fig. 4a . Poisson’s ratio ν was calculated as the ratio of the average compressive strains in the horizontal and vertical directions. Finally, average mechanical parameters that will be adopted for the homogenized masonry macro-modeling are grouped in Tables 4-5. The dilation angle and parameter were kept as in Section 4.1.

Fig. 3. Multi-scale modeling principle.

Fig. 4. Stress-strain curves of the RVE under (a) uniaxial compression; (b) uniaxial tension; (c) biaxial compression.

Table 4. Post-elastic behavior of the homogenized masonry. Category CDP Elastic parameters Parameter Kc fb0/fc0 Dilation angle (ψ) Elastic modulus (MPa) Poisson’s ratio Value 2/3 1,612 10° 392.15 0.11