Fast brick-based homogenized limit analysis for in- and out-of-plane loaded periodic masonry panels

This paper presents a 3D brick-based model that aims at the derivation of in- and out-of-plane homogenized failure surfaces for masonry. The considered masonry panel is discretized into regular parallelepiped 3D finite elements that are supposed to be rigid; the model here introduced uses a Kirchhoff-Love plate kinematics for the out-of-plane description of the displacement rate field of the elements. A linear programming problem formulated in standard form is scripted into Matlab to derive the in- and out-of-plane homogenized failure surfaces, also enabling the extraction of failure modes for the considered masonry element. The constraints of the linear programming problem come from the combination of an upper bound limit analysis problem and a homogenization-based approach. The proposed model is validated for two separate case studies: a running bond masonry test-window and an English bond masonry test-window. The homogenized failure surfaces resulting from the current model show good correspondence to those presented in three distinct works available in literature. Also, a few relevant failure modes are derived for the two case studies, and they are consistent with the expected deformed shapes at collapse for their related load conditions.