PSI - Issue 64

2242 Nicola Nisticò et al. / Procedia Structural Integrity 64 (2024) 2238–2245 Author name / Structural Integrity Procedia 00 (2019) 000–000 5 For dominant tensile loads, a discontinuity function ( ) is introduced. Loading-unloading and reloading are accounted (Figure 7). Equilibrium between macro and microplanes is enforced using the virtual work equation (Bažant and Prat, 1998), considering 28 microplanes for each hemisphere.

Figure 7. Loading-unloading and reloading rules. Microplane stress-strain relationship: (a) Volumetric; (b) deviatoric. (Gambarelli et al., 2016a)

3.1. Discrete and lattice model applications The initial applications of the Discrete Element Method (DEM) for masonry structures were presented in Nisticò (1994) and Pagnoni et al. (1993a,b). These studies focused on: failure analysis of brick walls subjected to in-plane lateral loading (Fig. 8); seismic analysis of a church (Fig. 9). Regarding lattice models: Fascetti et al. (2016a) introduced a randomly distributed lattice model to simulate Pultruded Glass Fiber-Reinforced Polymer (GFRP) I beams (Fig. 10a); Gaetani et al. (2019) proposed lattice approaches (Fig. 10b) to replicate the experimental tests conducted by Quadrino et al. (2018); Fascetti et al. (2018) developed a variant of the lattice discrete particle model for concrete (Fig. 11). This model was used in conjunction with a multiscale experimental procedure to evaluate various mechanical parameters for input.

Figure 8. In plane later loads. (a) Brick walls: effect of friction increasing in (Pagnoni, 1993a; Nisticò, 1994)

Figure 9. In plane later loads. (a) Brick walls: effect of friction increasing; (b) Collapse mechanism of a typical church (Pagnoni, 1993b; Nisticò, 1994)

Figure 10. (a) Web-flange behavior of pultruded GFRP I-beams: evolution of the crack pattern (Fascetti et al., 2016); (b) pointset, mesh, and results, illustrating the impact of varying percentages of random points (Gaetani et al., 2019).