Hybrid discrete-continuum multiscale modelling of masonry walls

The problem of modelling of the complexity of masonry walls is addressed, both at global (irregular shape and arrangement of openings) and microstructural (masonry texture) level. In the proposed hybrid approach, a masonry wall is modelled as a combination of discrete elements (rigid blocks interacting through nonlinear interfaces) [1] and continuum with microstructure (discretised through FEM). In the regions modelled as a continuum, the microstructure is accounted for by associating to each material element a Virtual Block Cluster (VBC) [2], i.e., a set of blocks representative of the periodic masonry texture. Depending on the kinematic assumptions within the VBC, the resulting continuum may behave as a homogenized or an enriched one. In a typical wall, the continuum model is adopted for all the regions where the masonry microstructure is regular, whereas the direct modelling of the microstructure as actual blocks is adopted where the periodicity is lost (e.g., arches or flat-arches, where the blocks are arranged in the peculiar voussoir-like fashion) or where a more accurate description of the microstructural behaviour is required [3]. The use of multiscale models for the continuum has a paramount advantage over more common phenomenological models (based on continuum plasticity, damage, smeared cracking, or a combination of these), which are increasingly complicated and require several parameters of uncertain determination. On the contrary, the complexity of the material behaviour is “distributed” between a relatively simple constitutive law for the interfaces (requiring only a few mechanical parameters) and the representation of the microstructural geometry. The mechanical model is implemented in the computer program SMARTmasonry (www.smartmasonry.it), which integrates a nonlinear solver for static and dynamics, a graphical user interface for data input, two-dimensional CAD functions, topology recognition for multi-connected domains, triangular and quadrilateral mesh generation algorithms, and a graphical post-processor. The relevance of the microstructural effects on the global behaviour, which is captured by the present approach, is shown by comparing numerical results of standard continuum and hybrid models in some study cases of walls with arch-supported openings. References [1] Salvatori, L., Spinelli, P., “Un modello discreto a deformabilità concentrata per strutture in muratura”, in Proc. WONDERmasonry 2, 11-12 October, Lacco Ameno - Ischia, 233-244 (2007). [2] Salvatori, L., Spinelli, P., “Homogenized and multiscale masonry models based on virtual block clusters”, in Proc. WONDERmasonry 3, 8-10 October, Lacco Ameno - Ischia, 655-665 (2009). [3] Salvatori, L., Spinelli, P., “Modellazione numerica ibrida di pareti in muratura”, in Proc. WONDERmasonry 4, 10-11 November, Firenze, 36-47 (2011).