Quasi-static analysis of an english-bond masonry structure: Two-step homogenized based approach vs macroscopic model

A two-step procedure based on homogenization theory is herein presented for the study of an English-bond masonry structure. Two simple and accurate homogenized based models are used to characterize the masonry behaviour via a representative volume element (RVE) defined at a structural level. One follows a FE micro-modelling approach within a Kirchhoff-Love plate theory and, the other, a Mindlin-Reissner formulation. Two three-dimensional micro-models are also presented, one homogeneous in the structure thickness and the other accounting for thickness discontinuities, to complement the data and allow wider conclusions. The procedure allows obtaining homogenized bending moment/torque curvature relationships to be used at a structural level within a FE discrete model implemented in a commercial FE code. The model relies in rigid quadrilateral elements interconnected by homogenized in-plane and bending/torque nonlinear springs. The masonry orthotropy and full softening behaviour are represented. The framework is used to study the behaviour of an English-bond masonry wall benchmark. Quasi-static analyses, with a mass proportional load, are performed. The numerical results are compared with a macroscopic approach and, when possible, with the experimental data. The results show that both out-of-plane shear stresses and the presence of vertical discontinuities have a key effect on the behaviour of the English-bond masonry structure. Recommendations are addressed.