In-plane failure surfaces for masonry with joints of finite thickness estimated by a Method of Cells-type approach

The macroscopic strength domain of in-plane loaded masonry walls is derived using an approach based on the upper bound theorem of limit analysis within the framework of homogenization theory. Following an approach similar to the Method of Cells for fiber-reinforced composites, a typical representative volume of masonry is subdivided into a few sub-cells, and a strain-rate periodic, piecewise differentiable velocity field, depending on a limited number of degrees of freedom, is defined. The ensuing approximated macroscopic failure surface is found to match with fair accuracy both available experimental data and theoretical predictions obtained by other authors with more refined numerical approaches. The proposed model is also applied to the prediction of the bearing capacity of a deep masonry beam: for any joint thickness, the criterion is found to give results as accurate as other complex numerical models, which take the heterogeneous nature of masonry into account. The model thus combines computational efficiency and accuracy.