Discrete and Continuous Models for Out-of-Plane Loaded Masonry Like Structures: A Multiscale Comparative Study

This paper presents a critical review of several analytical and numerical models that may be adopted for studying the out-of-plane behaviour of masonry structures having regular texture, with particular attention to the case of historical masonry, that is characterized by rigid blocks connected by mortar joints modelled as elastic interfaces. Discrete model, Love-Kirchhoff and Reissner-Mindlin plate models and a full three-dimensional heterogeneous finite element model are considered. The elastic parameters of both plate models are based on an existing compatible identification between a three-dimensional discrete model and two-dimensional plate models. Numerical tests are carried on by defining four case studies and paying attention to an in-plane scale factor, representing the size of heterogeneity of the masonry pattern, and to an out-of-plane scale factor, representing the thickness of the structure. Numerical tests show that the existing discrete model is simple and effective for representing masonry behaviour, especially when the magnitude of the heterogeneity is large with respect to the overall size of the panel. Increasing the in-plane scale factor, both plate models converge to the discrete one, but the Reissner-Mindlin plate model shows a better convergence and also allows the adoption of a simple plate finite element for performing numerical analysis.