PSI - Issue 84

Siro Casolo et al. / Procedia Structural Integrity 84 (2026) 1214–1221

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4. Numerical models developed 4.1. A HM-based strategy for modelling masonry, infill material and masonry-infill contact

The strategy adopted in this study is based on discretizing the heterogeneous materials of the masonry bridge (masonry, infill materials and masonry-infill contact) with a RBSM approach. The elementary cell of the computational model can be conceptually assimilated to the idea of a Heuristic Molecule (Casolo, 2021a), i.e. as an assembly of rigid elements (called “Heuristic Atoms”) interconnected by elasto-plastic springs. In this work, a “CSPF – Central, Shear and Polar Forces” type molecule has been adopted for the masonry, and an “SPF – Shear and Polar Forces” molecule for the infill (Figure 2). For communication purposes, the segment connecting the vertices shared by two neighbouring atoms (“first-order neighbours”) is defined as a “side-interface”, and the segment connecting the centers of two atoms that share a vertex (“second-order neighbours”) is defined as a “diagonal-bond”. The springs have been represented with different colours according to their role and constitutive response. The blue springs, which are axial and non-central, are arranged orthogonally to the interfaces and allow the axial and in-plane moment interaction between the atoms that are connected. The magenta shear springs are eccentric and parallel to the interfaces, allowing shear actions to be modelled. The red springs are central and arranged along the diagonals. They allow to model the central actions between atoms with higher-order contact and guarantee the modeling of Poisson effect under isotropic conditions. Since the infill is composed of loose granular material, =0 is assumed, and an isotropic molecule without diagonal springs (SPF) is adopted according to the HM approach (Casolo, 2021a). The contact between molecules of different types and, therefore, between masonry and infill, is modelled using only axial and shear springs (Figure 2).

Fig. 2. SPF and CSPF Heuristic Molecules: topology-HM assemblage; masonry and infill Heuristic Atoms assemblage with contact spring-bonds.

4.2. Discretization adopted for structural geometry The structural geometry has been discretized into 1,232 heuristic atoms with an approximate average side length of 0.75 m (Figure 1). A total number of 7,542 connections between the atoms have been considered for masonry, of 2,840 connections for the infill and of 344 connections for the masonry-infill contact. The base of the bridge model is constrained as shown in Figure 1. The impact forces are applied at the positions indicated in Figure 1, with impact angle measured as represented in the figure. The stress-strain laws assigned to the bonds-spring are shown in Figure 3. The elastic stiffnesses were determined using a principle of energy equivalence with a homogeneous and isotropic Cauchy continuum. The stiffnesses of the contact bond-springs, on the other hand, were obtained by averaging the values of the longitudinal elastic modulus between Masonry 1 and Infill and adopting a zero Poisson's ratio. The hysteretic laws of the bond-springs were defined in accordance with the experimental results available in the literature and considering a post-elastic phase such as to reproduce the behavior typically exhibited by masonry on a macro-scale: quasi-brittle collapse, accompanied by a markedly non-linear response, progressive decay of stiffness and strength, significant inelastic deformations and damage. The skeleton curve of the magenta springs is initially symmetrical. As the analysis proceeds, a loss of shear 4.3. Elastic response and hysteretic stress-strain laws adopted for bond-springs