This paper presents a multi-scale framework for the computational study of damage development in masonry walls, based on computational homogenisation techniques.
In order to overcome the troublesome formulation of closed-form constitutive equations, a first-order computational homogenisation framework is applied to infer the non-linear material behaviour of brick masonry in the presence of quasi-brittle damage of its constituents [
]. A localisation analysis is carried out based on the macroscopic homogenised tangent stiffness to capture the occurrence of localisation at the macroscopic scale [
]. It is shown that localisation is detected along preferential orientations, which are consistent with the underlying mesostructural failure patterns and with the applied loading.
An enhanced first-order computational multi-scale solution scheme is then outlined, which allows to incorporate microstructurally-based damage localisation orientations in structural computations. This model uses a first-order computational homogenisation technique enhanced with a finite width embedded damage band model in order to allow the treatment of macroscopic localisation resulting from damage growth in the constituents. The implementation of the multi-scale solution scheme using an nested finite element method is outlined. In particular, as a result of the use of homogenisation techniques on finite volumes in the presence of quasi-brittle constituents, mesostructural snap-back may occur in the homogenised material response. A methodology is proposed to introduce this response in the originally strain-driven multi-scale technique [
], based on energy dissipation control at the mesoscopic scale [
]. Its impacts on the implementation of the framework as well as on the path following techniques needed to trace complete load-deflection paths are discussed. The results obtained by the framework are illustrated by means of a strutural computation example.