Two-step homogenized elastic model for in-plane analysis of coated masonry walls

A two-step homogenization procedure is used to identify the (membrane) macroscopic elastic constants of coated masonry walls, solicited in their plane. The two steps deal separately with in- and out-of- wall plane homogenization, based on the modeling of an elementary cell by means of suitable designed assemblies of springs. As a result of the different step combinations, two homogenization strategies are derived. Both of them provide simple closed-form expressions for the linear elastic constants of an “equivalent” homogeneous and orthotropic material. The influence of the order of the homogenization steps is also investigated. Parametric analyses are carried out to examine the reinforcement effectiveness on the global behavior of the system. The accuracy of the theoretical results is assessed by comparisons with finite element (FE) models.