Simple homogenization models for the limit and non-linear analysis of masonry structures in- and out-of-plane loaded

The paper addresses the capabilities of kinematic and static models of masonry homogenization in the prediction of both the non-linear behaviour and the homogenized strength domains for in- and out-of-plane loads. The first approach is based on an equilibrated polynomial expansion of the micro-stress field into rectangular sub-domains within the elementary cell. The second is again a model based on equilibrium, and relies into a rough FE discretization of the unit cell through triangular elements with constant stress field (CST), where mortar joints are reduced to interfaces with frictional behavior and limited strength in tension and compression. The extension to out-of-plane loads is handled by means of a standard integration of the micro-stress field along the thickness. The generalization to the non-linear range is also very straightforward. The third procedure is kinematic identification strategy, 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 (MoC), where the Representative Element of Volume (REV) 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, 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. At a cell level, a critical comparison of pros and cons of all models is discussed, with reference to real cases