A couple-stress/cauchy multiscale model for the nonlinear analysis of periodic masonries under in-plane loading conditions

Concurrent multiscale approaches are suitable for studying the behavior of microstructured materials, since they combine the advantages of both macroscopic and microscopic approaches, i.e. the computational efficiency and the numerical accuracy, respectively. These models, which are based on a domain decomposition approach, have been recently employed also for the failure analysis of masonry structures, in the framework of the (Cauchy-based) first-order homogenization schemes. In the present work, an enhanced multiscale strategy for the nonlinear analysis of periodic masonries is proposed, based on the adoption of a couple-stress model at the macroscopic scale. This model, which can be regarded a constrained version of the Cosserat model, has been proved to capture the size effects usually experienced by these heterogeneous materials. On the other hand, a classical Cauchy model is employed at the microscopic scale, where damage phenomena are modelled by introducing cohesive interfaces at mortar joints. The proposed multiscale model is equipped with an adaptive strategy able to zoom-in automatically the zones affected by damage initiation; this strategy requires the determination of microscopically derived first failure surfaces in the space of the couple-stress macrostrains. The validity of the proposed multiscale approach is assessed by performing numerical simulations for different masonry panels subjected to complex in-plane loading conditions. In addition, suitable comparisons with direct numerical simulations are proposed.