Shell-3D multiscale modeling of masonry vaults based on the TFA procedure

This paper investigates the response of masonry-curved structural elements with periodic texture by adopting the modeling strategy recently developed by the authors (Addessi et al., 2021). Relying on a multiscale approach, the Mindlin−Reissner shell formulation is assumed at the macroscale and the classical 3D Cauchy continuum is adopted at the microscopic level to model the representative masonry unit cell (UC). The procedure for linking the two scales involves a transformation field analysis (TFA) homogenization technique based on piece-wise uniform distributions of the damaging and frictional mechanisms over the mortar joints. Advantages and limitations of this assumption are explored considering a masonry vault with stack bond texture, that is, assuming a UC made of one linear elastic brick surrounded by one head and one bed joint modeled as nonlinear interfaces. The more appropriate interface discretizations required by the TFA model are identified in relation to the activated deformation modes and the resulting computational effort is evaluated. Hence, an enriched TFA procedure is proposed to limit the computational cost and the time of analysis associated with the denser joint partitions, while still preserving the model accuracy. Finally, the efficiency of the model is investigated at the structural level by analyzing the response of the vault to differential settlements. The comparison between results obtained with the proposed multiscale formulation and those recovered by detailed micromechanical analysis confirms that the TFA approach is a very reliable and effective method for resorting to a fast reduced-order model also for curved geometries.