Dynamic Behaviour Analysis of an English-Bond Masonry Prototype Using a Homogenized-Based Discrete FE Model

Full Finite Element strategies (the so called micro- and macro- models) are still nowadays the most used ones for the study of large masonry structures. However, macro-modelling still lacks accuracy at a meso-scale in terms of damage localization. On the other hand, micro-models are rather computational demanding and require a cumbersome modelling stage. Thus, homogenization-based frameworks give considerable advantages. Moreover, the study of English bond masonry appears to be disregarded in comparison to the running bond one. On this behalf, a two-step procedure based on homogenization theory is herein presented for the dynamic study of English-bond masonry structures. The presented homogenization approach uses two models at a micro-scale: (i) a plane-stress FE discretization within the concepts of Kirchhoff-Love plate theory; and (ii) a three-dimensional micro-model accounting with the mortar joint discontinuity existent at the thickness direction. Bricks are meshed with elastic elements with linear interpolation and joints are reduced to interfaces which obey to the nonlinear behaviour described by the so-called combined cracking-shearing-crushing model. 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 code. The model relies in rigid quadrilateral elements interconnected by homogenized bending/torque nonlinear springs. The framework is used to study the dynamic behaviour of an English-bond masonry wall benchmark. A macroscopic strategy is also considered to enrich the study. The numerical results are compared with the experimental data and a good agreement has been found.