2D pixel homogenized limit analysis of non-periodic masonry walls

This paper presents a novel and straightforward procedure for the derivation of homogenized failure surfaces for non-periodic masonry. The most innovative feature of this procedure is the automatic generation of a convenient finite element mesh directly from the sketch of the considered masonry panel, based on the so-called “pixel strategy” that converts each pixel into an element. An upper bound limit analysis problem coupled with homogenization is then solved by aptly formulating it as a linear programming problem. Another main feature is the implementation of a reduced formulation of such problem (called “master-slave approach”) so that the number of unknown variables is reduced and, consequently, the computational times needed for the extraction of the homogenized failure surfaces are shortened as well. A simple procedure is also implemented for a quick identification of the statistical Representative Element of Volume (or REV) for a non-periodic masonry panel. The REV is the smallest portion of a composite material that includes all the physical and geometrical characteristics needed for its complete description. The reliability of the procedure is tested by investigating six case studies displaying different degrees of non-periodicity, extracting and critically commenting the results obtained in terms of homogenized failure surfaces and failure modes.