PSI - Issue 66

Domentico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 350–361 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 3. A masonry beam under a three-point bending test: (a) Geometry and boundary conditions. (b) Repeating Cell for the masonry

Table 1 summarizes the mechanical properties of the brick units and mortar joints.

Table 1. Material properties of the brick masonry couplets Property

Brick units

Mortar joints

Young's modulus E (MPa)

17500

3360

Poisson's ratio ν

0.15

0.2

Fracture Energy Gc (MPa) Tensile strength (MPa) Compressive strength (MPa)

- - -

0.002 0.086

7.26

The beam is investigated through a Direct Analysis (DA), which consists of modeling the entire geometry using the micro-modeling strategy described in Section 2.1 and the proposed concurrent adaptive multiscale model. In particular, Multiscale Analyses (MSA) are performed by assuming different scale factor (  ) values, precisely 1, 1.2, and 1.4. Fig. 3-b shows the RC selected for evaluating the homogenized mechanical property of the masonry to be adopted in coarser regions. Fig. 4-a and b show the computational mesh adopted to perform the DA and MSA analyses, respectively. As shown from the zoomed view of Fig. 3-a, brick units and mortar joints are discretized using a standard Delaunay type triangulation scheme. However, the former has a coarser mesh because the behavior of the brick units is assumed to be linearly elastic, while the latter is finer. In particular, the characteristic size of finite elements inside the mortar joints is equal to t m /  to ensure a sufficient discretization of the computational domain for accurately solving the phase-field problem. On the other hand, for the multiscale analysis, the geometry is initially discretized using linear macro elements of size equal to that of RC except for the boundary portions where kinematic and static conditions are imposed. Fig. 5-a and b show the results of the investigation. In particular, Fig. 5-a compares the results of DA and MSA in terms of vertical displacement of the top midspan point of the beam (  ) versus the applied force ( F ), whereas Fig. 5 b reports the computational times performing numerical simulations. The results show that the curves obtained using the proposed adaptive concurrent multiscale model almost overlap with those achieved by the DA, regardless of the value used for the scale factor   In particular, as shown in the zoomed view in Fig. 5-a, the MSA curves exhibit a jagged trend during their evolution. This behavior is likely due to the activation of fine regions within the computational domain during the numerical simulation, leading to sudden changes in local resolution and fluctuations in the computed results. However, this issue can be disregarded as it does not affect the accuracy of the numerical predictions.