A micro-macro homogenization for modeling the masonry out-of-plane response

This study introduces a finite element model based on a two-scale beam-to-beam homogenization procedure for the analysis of masonry structural members undergoing prevailing axial and bending stress states. The model is developed considering the periodic repetition of bricks and mortar joints in regular stack bond arrangement and assuming a linear elastic behavior for the former and a nonlinear response for the latter. At the microscopic heterogeneous scale, the behavior of a Unit Cell (UC) made of a single brick and mortar layer is described through an equivalent Timoshenko beam representation, where a nonlocal damage formulation with friction plasticity governs the mortar nonlinear constitutive relationship. Basing on a semi-analytical approach, the microscopic quantities are, then, homogenized to define an equivalent beam model at the macroscopic scale. The proposed finite element model is implemented in standard numerical codes to investigate the response of typical one-dimensional (1D) masonry elements. This study shows the numerical simulation of two experimental tests: a rectangular wallette under out-of-plane bending and a circular arch under vertical forces. The results obtained for the proposed model are compared with those resulting from micromechanical approaches and the experimental outcomes.