Masonry structures constitute a large portion of the built heritage around the world, from the past until today. Therefore, understanding their structural behavior is crucial for preserving the historical characteristics of many buildings and in addressing the requirements for housing and sustainable development. Due to its composite and highly nonlinear nature, the analysis of masonry structures has been a challenge for engineers. This article presents a set of advanced models for the mechanical study of masonry, including the usual micro-modeling approaches (the masonry constituents, unit and joint, are represented separately), macro-modeling (masonry constituents are smeared in a homogeneous composite), and multi-scale techniques (upscaling from micro to macro is adopted). An extensive overview of its computational features is provided. The engineering application of such strategies is presented and covers problems from the masonry components level (meso-scale) to the structural element itself, and ultimately to the level of monumental buildings (super-large). The structural safety assessment and/or strengthening schemes evaluation are performed amid the static, slow dynamics or earthquakes, and fast dynamics or impact and blast ranges.

This paper presents a simple and reliable homogenization approach coupled with rigid elements and homogenized interfaces for the analysis of out-of-plane loaded masonry panels. The homogenization approach proposed is a coarse finite element discretization wherein bricks are meshed with a few elastic constant stress triangular elements and joints reduced to interfaces with elastoplastic softening behavior with friction, tension cutoff, and a cap in compression. Flexural behavior is deduced from membrane homogenized stress-strain relationships through thickness integration (Kirchhoff–Love plate hypothesis). The procedure is robust and allows obtaining homogenized bending moment/torque curvature relationships (also in presence of membrane pre-compression) to be used at a structural level within a rigid body and spring mass model (RBSM) implemented in a commercial code. The model relies on rigid quadrilateral elements interconnected by homogenized bending/torque nonlinear springs. The possibility of extending the procedure to a finite element package, with standard built-in solution procedures, allows for a robust reproduction of masonry out-of-plane behavior beyond the peak load, in the presence of global softening. The procedure is tested on a set of windowed and full masonry panels in two-way bending. Excellent agreement is found with both experimental data and previously presented numerical approaches.