Three dimensional homogenization of masonry structures with building blocks of finite strength: A closed form strength domain

The present paper provides a straightforward methodology for the estimation in closed form of the overall strength domain of an in-plane loaded masonry wall by accounting for the failure of its bricks. The determination of the overall strength domain was based on a rigorous definition of the microstructure in, three dimensions on convex analysis and on the kinematical approach in the frame of limit analysis theory. No plane stress or plane strain assumption is a priori made. The formulation allowed distinguishing the yield surfaces that account for the failure of the joints and the yield surfaces that account for the failure of the building blocks. The validity and the efficiency of the derived analytical strength domain were investigated by means of numerical homogenization and experimental evidence. The proposed strength domain can be used in limit analysis approaches, in finite element simulations and for calibrating existing phenomenological models for masonry structures based on the micromechanical properties and the geometry of the bricks and the mortar.