PSI - Issue 44

Ylenia Di Lallo et al. / Procedia Structural Integrity 44 (2023) 488–495 Y. Di Lallo et al. / Structural Integrity Procedia 00 (2022) 000–000

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along the joints. The discretization strategy also entails the insertion of interface surfaces along the edges of the modules. An example of the assembly of modules for a brick wall with periodic arrangement is shown in Fig. 1(b), where the initial geometry of the wall is represented along with its discretised counterpart obtained from the MUDis procedure.

(a) (b) Fig. 1. The MUDis procedure: (a) elementary module; (b) example of module assembly on a masonry wall. Adapted from Brando et al. (2022) 2.2. The constitutive model of the interface elements While the units are considered linear elastic, the interface surfaces are defined by a constitutive model that describes the mechanical behaviour of both mortar joints and interface surfaces between mortar and units. In order to represent the non-linearity of the material, the CI (composite interface) constitutive model proposed by Lourenço and Rots (1997) was chosen as the most suitable. This model, also known as “combined crack-shearing-crushing model”, consists of a Coulomb friction model for shear failure, combined with a tension cut-off for the failure in tension and an elliptical cap for the compressive failure. Conceived for simplified micro-modelling strategies, this formulation might lead to inaccurate results with the proposed MUDis approach, given the reduced - and geometrically different - number of units and the pre-established failure surfaces involved in the discretization. These reasons called for the necessity to modify some of the key parameters that define the CI formulation. The development of this modified composite interface model involved a three-stage process, as described in Brando et al. (2022): • Step 1: Parametric analysis to identify the parameters of the CI model relevant for the MUDis approach; • Step 2: Development of a mathematical model to define the transformation relationships necessary to modify the identified CI parameters into analogous features suitable for the MUDis-based modelling approach; • Step 3: Numerical calibration analyses to determine the final set of optimal relationships correlating each parameter of the MUDis-based model with the original parameter of the CI model. The first step was devoted to carrying out a remarkable number of numerical analyses in order to identify the key parameters of the CI formulation that govern the response of diverse periodic masonry walls under horizontal loading. Based on the results obtained from this step, three parameters were chosen as fundamental to describe the behaviour of the new interface elements featured by the MUDis-based models: tensile strength ( σ tra ), cohesion (c) and friction