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.