Implementation and validation of a total displacement non-linear homogenization approach for in-plane loaded masonry

Two simple homogenization models suitable for the non-linear analysis of masonry walls in-plane loaded are presented. A rectangular running bond elementary cell is discretized by means of twenty-four constant stress three-noded plane-stress triangular elements and linear two-noded interfaces. Non-linearity is concentrated on mortar reduced to interface, exhibiting a holonomic behavior with softening. The paper shows how the mechanical problem in the unit cell can be characterized by very few displacement/stress variables and how homogenized stress-strain behavior can be evaluated by means of a small-scale system of non-linear equations. At a structural level, it is therefore not necessary to solve a homogenization problem at each load step in each Gauss point and a direct implementation into commercial software as an external user supplied subroutine is straightforward. Non-linear structural analyses are conducted on a variety of different problems, for which experimental and numerical data are available in the literature, in order to show that accurate results can be obtained with a limited computational effort.