Homogenized non-linear dynamic model for masonry walls in two-way bending

A simple homogenization approach accounting for mortar joint damaging is presented, suitable to analyse entire panels in two-way bending in the non-linear dynamic field. A rectangular running bond elementary cell (RVE) is subdivided into several layers along the thickness and, for each layer, a discretization where bricks are meshed with plane-stress three-noded triangular elements and joints are reduced to interfaces with damaging behaviour is assumed. Non linearity is due exclusively to joints cracking, which exhibit also a frictional behaviour with limited tensile and compressive strength with softening. A damaging material is utilized for joints in order to properly take into account the actual opening and closure of cracked mortar under cyclic loads. Finally, macroscopic curvature bending moment diagrams are obtained integrating along the thickness in-plane micro-stresses of each layer. Homogenized masonry flexural response under load-unload conditions is then implemented at a structural level in a FE non-linear code based on a discretization with rigid three-noded elements and elasto-damaging interfaces where elastic and inelastic deformation is allowed only for flexural actions. The two step model proposed is validated both at a cell and structural level, comparing results obtained with both experimental data and existing macroscopic numerical approaches available in the literature