Numerical analysis and modelling of the damage and softening of brick masonry

Abstract

Despite its texture as a periodic composite material, masonry is generally modelled as a ‘concrete-like’ material, so that its anisotropic nature is not taken into account. A way to derive an enhanced constitutive model for masonry, closely related to the behaviour of its constituent materials (mortar and bricks) and to its geometry (bond pattern, thickness of the mortar joints, etc.), is to take advantage of the homogenization techniques, which have been extensively developed for composite materials. Among them, the homogenization theory for periodic media seems particularly suitable. According to this theory, the global behaviour of masonry may be derived by solving a boundary value problem on a small domain to be repeated by translation (cell) with particular boundary conditions (periodicity) and special type of loading (average of strain and/or stress). This problem turns out to be generally well posed: in linear elasticity, it yields the macroscopic elastic characteristics of masonry (in the case of running bond masonry, the four constants defining the equivalent orthotropic material) [1]. In the non-linear range (damage or plasticity), it may be used to determine the failure criterion of the homogenized material: in the stress (or strain) space, radial loading paths are imposed and, for each direction considered, the maximum stress, the corresponding strain and the pattern of failure are determined.