SUMMARYThis 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.

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This contribution deals with the application of computational homogenization techniques for structural masonry computations, as an alternative to the formulation of complex closed-form macroscopic constitutive laws. The complexity of modeling masonry material stems from the anisotropy evolution and localization induced by mesostructural damage. This phenomenon appears with preferential damage orientations, which are intimately related to the initial periodic structure of the material. The upscaling procedure used here relies on the formulation of mesoscopic constitutive laws at the level of the individual brick and mortar materials. A mesostructural unit cell with its corresponding periodicity requirements is used to deduce the average response of the masonry material through a scale transition. At the macroscopic scale, this averaged material response is used in the frame of an enhanced continuum approach with embedded localization bands, the widths of which are directly deduced from the initial periodicity of the material. The results obtained by the framework are illustrated and discussed by means of a structural computation example, which involves a complex cracking evolution together with fully anisotropic damage development.