A micro-mechanical model for the homogenisation of masonry

Masonry is a composite material made of units (brick, blocks, etc.) and mortar. For periodic arrangements of the units, the homogenisation techniques represent a powerful tool for structural analysis. The main problem pending is the errors introduced in the homogenisation process when large difference in stiffness are expected for the two components. This issue is obvious in the case of non-linear analysis, where the tangent stiffness of one component or the tangent stiffness of the two components tends to zero with increasing inelastic behaviour. The paper itself does not concentrate on the issue of non-linear homogenisation. But as the accuracy of the model is assessed for an increasing ratio between the stiffness of the two components, the benefits of adopting the proposed method for non-linear analysis are demonstrated. Therefore, the proposed model represents a major step in the application of homogenisation techniques for masonry structures. The micro-mechanical model presented has been derived from the actual deformations of the basic cell and includes additional internal deformation modes, with regard to the standard two-stephomogenisation procedure. These mechanisms, which result from the staggered alignment of the units in the composite, are of capital importance for the global response. For the proposed model, it is shown that, up to a stiffness ratio of one thousand, the maximum error in the calculation of the homogenised Young’s moduli is lower than five percent. It is also shown that the anisotropic failure surface obtained from the homogenised model seems to represent well experimental results available in the literature