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