Microstructural, homogenised, and multiscale models for masonry structures based on rigid blocks

A microstructural model for masonry based on rigid blocks is used for deriving a continuum homogenised model. The constitutive behaviour of the continuum material element is obtained through the virtual power equivalence with an aggregate of rigid blocks that reproduce the microstructure in a representative volume. We call this set of blocks ‘Virtual Block Cluster’ (VBC) in analogy to the virtual atomic cluster technique developed for molecular dynamics. The continuum model, either Cauchy’s or a richer one, is discretised through standard finite elements, so that a VBC is associated with each integration point. Numerical examples are presented and the results obtained through the continuum model based on VBC are compared to those obtained through the explicit modelling of the microstructure. In order to solve the cases of local microstructural heterogeneities and of strain localisations, both precluded to homogenised models, two distinct multiscale approaches are developed and implemented.