Multiscale analysis of out-of-plane masonry elements using different structural models at macro and microscale

A novel two-scale modeling approach, linking different structural models at macro and microscale, is proposed to describe response of masonry walls with periodic texture. At the higher macroscopic scale, the real heterogeneous material is modeled as a homogenized medium, considering the classical Mindlin-Reissner theory for flat shells. At the lower microscopic scale, a representative masonry Unit Cell (UC), accounting for the actual geometry, arrangement and nonlinear behavior of constituent materials, is analyzed in detail by resorting to a three-dimensional Cauchy model. The UC is modeled as the assembly of elastic bricks and nonlinear zero-thickness interfaces, in which the sliding frictional and damaging mechanisms are concentrated. To perform the macro–micro information transition a proper kinematic map is defined, whereas the upscaling process is performed via a homogenization procedure based on the Transformation Field Analysis (TFA), properly extended to the case of interfaces. The developed homogenization procedure invokes a generalized Hill-Mandel principle and requires to satisfy ‘non-standard’ constraints at the microlevel, for which the perturbed Lagrangian method is employed. Numerical applications are performed to prove the model efficiency in describing the response of a running bond UC subjected to in-plane and out-of-plane loads. Special attention is devoted to the analysis of shell bending and shear behavior, comparing the results obtained with the proposed model with those recovered by detailed micromechanical analyses.