The masonry is a traditional building material that has been used throughout history and is still used today. The masonry is the main construction technique adopted in historic structures, and a deep understanding of their behavior is vital for the preservation of our cultural heritage. Despite its widespread use, the masonry has been frequently used by adopting an empirical approach due to poor knowledge of the complex mechanical behavior of this type of composite material.

Advanced numerical methods are attractive tools for understanding and predicting the behavior of the masonry until failure. They allow the estimation of the residual resistance and the safety of structures. In recent years, they have been proposed different computer models, based either on a micro-modeling full of the constituents of the material (bricks and mortar joints), or in macro-phenomenological models. From these two approaches, computational homogenization methods have recently emerged as a promising tool that can combine the advantages of micro- and macro-modeling. The problem is divided into two steps: the structural scale is treated as an equivalent homogeneous medium, while the complex behavior of heterogeneous microstructure is taken into account by solving a micro-mechanical traceable to a representative sample of the microstructure problem. The aim of this research is the development of a computational technique for homogenisation multi-scale analysis of masonry structures under quasi-static horizontal loads acting on the plane and out of plane.

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