A simple homogenized orthotropic model for in-plane analysis of regular masonry walls

Simple closed-form expressions for “equivalent” linear elastic constants of regular brick pattern masonry, solicited in their plane, are derived by means of a homogenization procedure. The stresses of the brick and mortar components are also evaluated analytically once the average stress acting on the homogeneous medium is determined. The fundamental concept of the method consists of modeling the behavior of a masonry cell using suitable designed assemblies of in-series and in-parallel springs. Thereafter, an equivalent homogeneous and orthotropic material is defined, the elementary cell of which has the same stiffness as the assembly. As a further simplified model, an equivalent isotropic material is defined. The accuracy of the theoretical results is assessed by means of comparisons with finite element (FE) analyses drawn from the literature. The proposed approach is found to match the macroscopic linear elastic laws of the literature accurately, with the advantage of taking a far simpler form. Finally, static and dynamic FE analyses are carried out on sample masonry walls, with the aim of comparing the non-homogeneous and homogeneous models. The latter is found to describe both the local and global behavior of masonry walls to a satisfactory extent.