Derivation of the out-of-plane behaviour of masonry through homogenization strategies: Micro-scale level

Two simple and reliable homogenized models are presented for the characterization of the masonry behaviour via a representative volume element (RVE) defined at a structural level. An FE micro modelling approach within a plate formulation assumption (Kirchhoff-Love and Mindlin-Reissner theory) using Cauchy continuum hypotheses and first-order homogenization theory is adopted. Brick units are considered elastic and modelled through quadrilateral finite elements (FEs) with linear interpolation. Mortar joints are assumed to be inelastic and reduced to zero-thickness interface FEs. A multi-surface plasticity model governs the strength envelope of mortar joints. It can reproduce fracture, frictional slip and crushing along the interface elements, hence making possible the prediction of a stepped, toothed or de-bonding failure pattern of masonry. Validation tests on the homogenized procedures are undertaken to conclude on the correct identification of the elastic stiffness properties, in the ability to reproduce the masonry orthotropic behaviour and the effect of potential pre-compressive states. Furthermore, the approaches are extended to characterize a case study of an English-bond masonry wall. Both the validation and application steps provide excellent results when compared with available experimental and numerical data from the literature. Conclusions on the influence of three-dimensional shear stresses and the effect of potential discontinuities along the thickness direction are also outlined. The two homogenized approaches are, for the running- and English-bond masonry cases, integrated within a FE code. By providing reliable and low computational cost solutions', these are particularly suitable to be combined within multi-scale approaches. (C) 2018 Elsevier Ltd. All rights reserved.