An enhanced multi-scale approach for masonry wall computations with localization of damage

This contribution presents a multi-scale framework for the computational study of masonry structures. In order to overcome the need for excessively complex closed-form constitutive equations, a first-order computational homogenization framework is applied to infer the non-linear material behaviour of brick masonry in the presence of quasi-brittle damage. A localization analysis is carried out based on the macroscopic homogenized tangent stiffness. It is shown that localization is detected along preferential orientations, which are consistent with the underlying mesostructural failure patterns and with the applied loading. The macroscopic description is enhanced with a finite width damage band model in order to allow the treatment of macroscopic localization resulting from damage growth in the constituents. As a result of the use of homogenization techniques on finite volumes and the presence of quasi-brittle constituents, mesostructural snap-back may occur in the homogenized material response. A methodology to introduce this type of response in the multi-scale technique is proposed. The numerical implementation of the multi-scale solution scheme using a finite element method is outlined. The results obtained by the framework are illustrated by means of elementary examples, and by an example of a structural wall computation.