A mixed micromechanical homogenisation scheme for the prediction of the 3D orthotropic elastic properties of different masonry bond typologies

Abstract

Masonry structures composed of two distinct material phases (units and mortar) with potentially vastly different elastic properties are characterised by strong orthotropy. The variety of commonly employed bond typologies for masonry walls, featuring unit groups and mortar joints with different orientation with respect to the plane of the wall, result in complex stress and strain interactions between the material phases. This interaction is further complicated by the high volume ratio of the units within the masonry composite. Therefore, classical homogenisation schemes for matrix-inclusion composite materials, mortar being the matrix and units the inclusions, are suitable for only a narrow range of relative unit and mortar stiffness, expressed as the ratio of the Young’s moduli of the two phases. This feature makes their application in nonlinear analysis of masonry structures, which have a strong tendency to crack under mechanical loading, problematic.The paper presents a novel homogenisation scheme based on different mean-field homogenisation schemes combined through a process derived from the discretisation of the masonry cells using a method-of-cells approach. This approach allows the intuitive interpretation of the stress and strain interaction of the material phases and yields good predictions of the elastic properties of a variety of masonry bonds over an extensive range of relative unit and mortar stiffness.