Closed form homogenization model for masonry in-plane loaded

A holonomic homogenization model suitable for the non-linear analysis of masonry walls in-plane loaded is presented. A rectangular running/header bond unit cell is discretized by means of 24 constant stress, three-noded plane-stress triangular elements and interfaces. Non linearity is concentrated on mortar reduced interface, obeying a holonomic relationship with softening. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how the homogenized masonry behavior is directly deducible from the unit cell problem directly at a structural level by means of a pseudo analytical approach. At a structural level the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). In order to validate the proposed homogenization model, three distinct series of simulations are conducted with respect to some laboratory walls. All the non-linear analyses discussed in the present paper have been performed using the commercial software Abaqus, where the stress-strain homogenized relationships were directly implemented. The purpose of the authors is to show how reliable results may be obtained at a very limited computational effort.