Simple lower bound limit analysis homogenization model for in- and out-of-plane loaded masonry walls

A simple homogenized equilibrated and admissible model for the limit analysis of masonry walls in- and out-of-plane loaded is presented. A rectangular running bond elementary cell (RVE) is discretized by means of a few constant stress triangular elements (CST) and interfaces. Non linearity is concentrated on brick–brick interfaces and joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength. When dealing with the flexural behavior, a Kirchhoff–Love homogenized model is derived, subdividing the REV into several layers along the thickness and in discretizing each layer analogously to the in-plane case. When dealing with the in-plane behavior, a linear programming problem with very few variables is obtained, which can be handled even manually for some cases of technical interest. The lower bound model proposed is validated at a cell level through literature kinematic models, to show that the lower bound approach provides almost identical results with respect to upper bound approaches, meaning that the actual solution is well approximated. Homogenized masonry behavior is then implemented at a structural level in consolidated FE limit analysis codes for the evaluation of collapse loads and failure mechanisms of real scale masonry structures.