Homogenisation of masonry structures subjected to seismic loads through matrix/inclusion micromechanics

The mechanical properties of masonry, both in the linear elastic range and after the onset of damage, are dependent on the geometric and mechanical properties of its constituent materials: the units and the mortar. Finite element micromodelling, while capable of providing accurate and comprehensive results, is associated with high computational costs and modelling effort. On the other hand, micromechanical homogenisation of the masonry composite provides an attractive alternative to detailed micromodelling, in which the stress and strain interaction between the material phases can be modelled without excessive computational cost and in which interpretation of the damage state of the phases is more straightforward. However, nonlinear micromechanical homogenisation of masonry elements through varied numerical and analytical approaches remains a subject of intense study. In this paper, an inclusion-based homogenisation scheme for masonry structures is proposed for plane stress conditions. The scheme is combined with constitutive laws for damage in the constituent materials of the masonry composite and implemented in finite element models. The proposed modelling approach is validated in terms of its capacity to predict the elastic properties against experimental results and a finite element benchmark. Finally, finite element analyses of walls subjected to in-plane shear under varying levels of vertical stress are performed and favourably compared with experimental results in terms of predicted capacity and obtained failure mode. The low computational cost of the proposed model makes it suitable for future application in digital twinning operations.