# Department of Mechanics: Seminar: Abstract Milani

##### Gabriele Milani (Politecnico di Milano, Italy)

#### Comparison between Upper and Lower Bound Strategies to Determine Masonry Homogenized Strength Domains

In the seminar, four simple models by the speaker for the determination of the homogenized strength domain of running bond masonry in-plane loaded are reviewed and critically 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 sub-cells with pre-assigned polynomial fields of periodic-velocity. The first and the latter model 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 real case studies. A generalization to out-of-plane loads is also introduced.