PSI - Issue 79

Mansi Gupta et al. / Procedia Structural Integrity 79 (2026) 259–265

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Table 1. Dimensions of the beams [Zhu et al. (2024), Trawi ń ski et al. (2016), Trawi ń ski et al. (2018), Bhowmik and Ray, (2019)] Designation Span (S) Length (L) Depth (D) Width (B) Notch size (a 0 ) (mm) (mm) (mm) (mm) (mm) B1 240 320 80 40 8 B2 200 300 50 50 10 B3 400 550 100 50 20 B4 800 1000 200 50 40 2.2. Constitutive behavior and material properties In finite element modelling, two types of elements are used: bulk elements and cohesive elements (Kargari et al. (2023)). The bulk elements represent the continuum material and follow linear-elastic constitutive behavior, while the cohesive elements enable the simulation of crack initiation and propagation, governed by a traction separation law. The Young’s modulus (E) and Poisson ratio ( υ ) vales for the FE model are kept in accordance with the 2D simulation of mesoscale beams by Trawi ń ski et al. (2016). Accordingly, three types of bulk elements are used in the present study for mesoscale aggregates and mortar and for homogeneous regions of the beam. For the traction separation law in cohesive elements, the constitutive behavior is defined in terms of traction (f), stiffness (k), and separation ( δ ) in normal and tangential direction. The initial stiffness in both normal and tangential direction is taken as k 0 = 10 6 (MPa/mm) (Trawi ń ski et al. (2016)). The tensile strength (f n ) parameters for mortar matrix and ITZ region is employed as 4.4 and 1.6 MPa, respectively (Skar ż y ń ski et al. (2015)). A quadratic damage initiation criteria (QUADS) is used for damage modelling with effective relative displacement at complete decohesion ( �� ) as 0.071 mm for mortar elements and 0.098 mm for ITZ elements (Trawi ń ski et al. (2016)). The exponential softening parameter ( α ) is kept same as 7.5 in both the types of cohesive elements and fracture energy (G F ) is kept as 0.04 and 0.02 N/mm for mortar and ITZ, respectively (Trawi ń ski et al. (2016)). These material properties are summarized in Table 2. Table 2. Material properties used in FE model (Zhu et al. (2024), Trawi ń ski et al. (2016)) Solid Elements Constants Aggregates Mortar Matrix Homo. region E (MPa) 47200 29200 36100 υ (-) 0.2 0.2 0.2 Cohesive Elements Constants Mortar Matrix ITZ k 0 (MPa/mm) 10 6 10 6 f n (MPa) 4.4 1.6 G F (N/mm) 0.04 0.02 α (-) 7.5 7.5 �� (mm) 0.071 0.098 2.3. Mesostructure generation In this study, the aggregates are generated and placed in the meso domain using Take and Place method by (Wang et al., 2015a, 2015b). The gradation of aggregates was determined using the Fuller curve (Wriggers and Moftah, 2006), with aggregate area in the corresponding sieve size calculated as: � � ��� � � � � � ��� � � � � � � ��� � � � ��� � � � � where, � � ��� � � � is the aggregate area within the sieve diameters ��� and � . P(d) is cumulative passing percentage. ��� and ��� are the maximum and minimum sieve sizes, respectively. � is the ratio of aggregate area to domain area, and A is the mesostructure domain area. The procedure for generating aggregates by Take and Place method is explained below. In the first step, key parameters such as aggregate size distribution, volume ratio, maximum and minimum aggregate size, minimum distance between each aggregates and the minimum distance of aggregate from domain boundary are specified.