Nonlinear discrete homogenized model for out-of-plane loaded masonry walls

This paper presents a simple and reliable homogenization approach coupled with rigid elements and homogenized interfaces for the analysis of out-of-plane loaded masonry panels. The homogenization approach proposed is a coarse finite element discretization wherein bricks are meshed with a few elastic constant stress triangular elements and joints reduced to interfaces with elastoplastic softening behavior with friction, tension cutoff, and a cap in compression. Flexural behavior is deduced from membrane homogenized stress-strain relationships through thickness integration (Kirchhoff-Love plate hypothesis). The procedure is robust and allows obtaining homogenized bending moment/torque curvature relationships (also in presence of membrane pre-compression) to be used at a structural level within a rigid body and spring mass model (RBSM) implemented in a commercial code. The model relies on rigid quadrilateral elements interconnected by homogenized bending/torque nonlinear springs. The possibility of extending the procedure to a finite element package, with standard built-in solution procedures, allows for a robust reproduction of masonry out-of-plane behavior beyond the peak load, in the presence of global softening. The procedure is tested on a set of windowed and full masonry panels in two-way bending. Excellent agreement is found with both experimental data and previously presented numerical approaches.