3D voxel homogenized limit analysis of single-leaf non-periodic masonry

This paper presents an extensive investigation on the out-of-plane collapse behavior of single-leaf non-periodic masonry walls. This is achieved by deriving out-of-plane homogenized failure surfaces from test-windows that are extracted from various location within the same non-periodic masonry wall. The concept of “test-window” is inspired by that of Statistically Equivalent Periodic Unit Cell (SEPUC), which is an evolution of that of Representative Element of Volume (REV), and is needed for successfully applying homogenization to non-periodic masonry. An innovative feature introduced in this paper is the automatic generation of a suitable 3D finite element mesh directly from the sketch of the considered masonry test-window, based on a so-called “voxel strategy” that converts each voxel (the 3D equivalent of a pixel) into a finite element. Moreover, this mesh generating procedure enables the correct representation of the transversal layout of the test-window, and it also contains a coarsening strategy that allows a reduction of the overall number of finite elements in the 3D mesh. For the derivation of the out-of-plane homogenized failure surfaces a linear programming problem is solved, which is based on the upper bound theorem of limit analysis coupled with a homogenization approach. The investigation is performed on six real case studies displaying different degrees of non-periodicity: for the four test-windows of each case study, two out-of-plane homogenized failure surfaces are extracted (flexural and torsional) as well as three relevant deformed modes at collapse. Eventually, the results are critically commented; comparisons are drawn among the case studies, highlighting the influence of each non-periodic masonry bond on the results.