Four approaches to determine masonry strength domain

Four models to determine the homogenised strength domain of running bond masonry in-plane loaded are compared. The first is a lower bound, where the elementary cell is subdivided into a few rectangular sub-domains and 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 constant stress triangular elements. The third procedure is a compatible identification (kinematic approach), where joints are reduced to interfaces and bricks are assumed infinitely resistant. The last model is again a kinematic procedure based on the so-called method of cells. The representative element of volume is subdivided into six rectangular sub-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, still allows considering failure inside bricks. The third approach is the most straightforward, but is reliable only for thin joints and strong blocks. Some illustrative examples regarding the determination of masonry homogenised strength domains are discussed, focusing on pros and cons of the models, role played by joint thickness, constituent materials failure surfaces and numerical efficiency.