Homogenized and Multiscale Masonry Models Based on Virtual Block Clusters

A multiscale model for masonry, based on rigid-block microstructure is presented. The homogenised material is treated as a continuum, whose constitutive behaviour is derived from the virtual power equivalence of the material element with an aggregate of rigid blocks that reproduces the microstructure in a representative volume. We call this set of blocks ‘Virtual Block Cluster’ (VBC). 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 provided and the simulation results of the continuum model based on VBC and of the explicit direct modelling of the microstructure are compared. Finally two multiscale approaches, in which the homogenised continuum and the direct modelling of microstructural details coexist, are considered. The first one is based on domain partitions, where the two scales are are used in different regions, whereas the second one superimposes the actual microstructure to the homogenized continuum. Each multiscale approach solves a case precluded to homogenised models: the presence of local microstructural heterogeneities (through domain partition) and strain localisations (through concurrent modelling).