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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resolution model ( i.e. , a macro-modeling strategy) in regions where the masonry is expected to behave as linear elastic and a finer-resolution model ( i.e. , micro-modeling strategy) in areas where detailed analysis is required due to significant stress concentrations or damage development. Specifically, inside the coarse regions, the masonry is modeled through linear elastic macro-elements whose constitutive behavior is obtained by performing a first-order homogenization analysis on a Repeating Cell (RC) of the masonry. On the other hand, inside finer regions, the masonry is represented using a micro-mechanical model that accurately reproduces failure mechanisms. In particular, the Phase Field Cohesive Zone Model (PF-CZM) for fracture is adopted to reproduce the fracture mechanisms inside the masonry (Wu (2017), Wu and Nguyen (2018), Chen and Wu (2022)). The adaptive nature of the model is highlighted by the progressive activation of finer regions within the computational domain as damage mechanisms develop in the coarse regions. This activation occurs when conditions defined by an appropriate activation criterion are met. The rest of the paper is structured as follows: Section 2 summarizes the theoretical aspects at the base of the proposed model and details the numerical implementation aspects. Section 3 presents the numerical results that validate the proposed strategy, and Section 4 outlines the main conclusions of the work. 2 Theoretical background This section reports the main theoretical concepts at the base of the proposed adaptive concurrent multiscale model. First, an exhaustive description of the micro- and macro-modeling strategy adopted for reproducing the behavior of the masonry inside the finer and coarser regions of the computational domain is provided. Subsequently, the activation criterion adopted to activate the finer regions inside the computational domain is described. The concept of the first failure surface for the masonry is introduced in such a framework. 2.1 Micro-modeling strategy for reproducing the failure behavior of the masonry Consider a two-dimensional periodic masonry structure composed of regular brick units bonded through vertical and horizontal mortar joints (Fig. 1-a). The structure occupies the 2D region   R 2 , whose external boundary  comprises two disjoint parts  t and  u , i.e. ,  t ∩  u =  , on which given Neumann and Dirichlet and boundary conditions are applied, respectively. Specifically, external tractions t act on  t , while prescribed displacements u are imposed on  u . The brick units are assumed to behave as linear elastic ( i.e. , undamageable), whereas the mortar joints are potentially damageable.

Fig. 1. (a) A schematic of a regular brick masonry structure. (b) Identification of a Repeating Cell for the periodic masonry

In the proposed model, the fracture mechanisms of mortar joints are reproduced using the Phase Field Cohesive Zone Model (PF-CZM), initially proposed by Wu et al. (Wu (2017)). The basic idea of the PF-CZM is to represent a sharp crack as a band of finite width, in which the amount of damage is described through a continuous scalar field