`A multiscale approach for the analysis of block masonry under damage and friction’

The topic of this paper is the numerical analysis of periodic masonry brickwork seen at a microscopic level as a set of blocks interacting through non linear elasto-plastic softening interfaces. Two approaches are generally used in the literature in order to describe such a behaviour: Dicrete Models, aiming at the detailed solution of the microscopic problem, but characterized by very high computational costs, and Contunumm Models, providing a coarse description of the masonry material but perfectly fit for a coarse FEM discretization. It is our opinion that, when the analysis of a whole masonry building is the primary goal, the use od Discrete Models is practically prohibitive. However, the use of Contuinuum Models implies the definition of a carefully tuned constitutive prescription, possibly based on a microscopic analysis of the masonry material. A different approach, known as Multi-scale Method, is proposed in this work. This method does not define any constitutive relation at the macroscopic level, but adopts a step-by-step homogenization technique that takes into account the presence of both micro and macro models throughout all the integration procedure.