An Adaptive Concurrent Multiscale Approach Based on the Phase-Field Cohesive Zone Model for the Failure Analysis of Masonry Structures

Simulating damage phenomena in masonry structures remains a significant challenge because of the intricate and heterogeneous nature of this material. An accurate evaluation of fracture behavior is essential for assessing the bearing capacity of these structures, thereby mitigating dramatic failures. This paper proposes an innovative adaptive concurrent multiscale model for the failure analysis of masonry structures under in-plane loading conditions. Developed within a Finite Element (FE) framework, the proposed model employs a domain decomposition scheme to solve a combination of fine- and coarse-scale sub-models concurrently. In regions requiring less detail, the masonry is represented by homogeneous linear elastic macro-elements. The material properties for these macro-elements are derived through a first-order computational homogenization strategy. Conversely, in areas with higher resolution needs, the masonry is modeled as a heterogeneous material, accurately depicting individual brick units and mortar joints. To capture strain localization effectively in these finer regions, a Phase Field Cohesive Zone Model (PF-CZM) formulation is employed as the fracture model. The adaptive nature derives from the fact that at the beginning of the analysis, the model is entirely composed of coarse regions. As nonlinear phenomena start to develop, these regions are progressively deactivated and replaced by fine regions. An activation criterion detects damage-prone portions of the domain, thus triggering the transition from macro to micro scales. The validity of the proposed model is assessed through multiscale numerical simulations on a specific case study, with the results compared to those from a direct numerical simulation. The results confirm the effectiveness and accuracy of this innovative approach for analyzing masonry failure.