Comparison between Upper and Lower Bound strategies to determine the homogenized strength domain of running bond masonry in-plane loaded

Four models for the determination of the homogenized strength domain of running bond masonry in-plane loaded are compared. The first is a lower bound approach, where the elementary cell is subdivided into a few rectangular sub-domains, where the micro-stress field is expanded using polynomial expressions. The second is again a lower bound, where joints are reduced to interfaces and bricks are subdivided into a few constant stress triangular elements (CST). The third procedure is a compatible identification, which belongs to the upper bound family, where joints are reduced to interfaces and bricks are assumed infinitely resistant. The last model is again a kinematic (upper bound) procedure based on the so called Method of Cells (MoC), where the elementary cell is subdivided into six rectangular cells with pre-assigned polynomial fields of periodic-velocity. The first and latter models have the advantage that the reduction of joints to interfaces is not required. The second approach, albeit reduces joints to interfaces with frictional behavior, still allows to consider failure inside bricks. The third approach is the most straightforward, but is reliable only in case of thin joints and strong blocks. A critical comparison of pros and cons of all models is discussed, with reference to a real case study.