Homogenization of heterogeneous masonry beams

This paper presents two micromechanical and a multiscale two-dimensional finite element models for the analysis of masonry walls under out-of-plane instability effects. The micromechanical analysis are performed considering elastic beams to model the bricks and either nonlinear beams or interfaces to model the mortar layers. The beam finite elements rely on the force-based formulation and account for large displacements by making use of the corotational approach. This latter is properly formulated and extended to interface elements to include nonlinear geometry effects. The multiscale model is defined by applying a two-scale beam-to-beam homogenization procedure, developed for masonry elements with periodic bricks arrangements. Hence, a Unit Cell made of a single linear elastic brick and a single nonlinear mortar layer is introduced at the microscopic level, which is linked to the macroscale level through a semi-analytical homogenization technique. In all models, a damage formulation with friction plasticity governs the mortar constitutive relationship. Computational details on model implementation and solution procedures are given for all approaches. Correlation studies are performed to assess the proposed numerical micromechanical and multiscale procedures. In particular, the behavior of an unreinforced wall tested under vertically eccentric load is reproduced and advantages and disadvantages of proposed approaches are discussed