[en] In a context of restoration of historical masonry structures, it is crucial to properly estimate
the residual strength and the potential structural failure modes in order to assess the safety of
buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry
presents preferential damage orientations, strongly localised failure modes and damage-induced
anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry
structures are generally subjected to complex loading processes including both in-plane and out-
of-plane loads which considerably influence the potential failure mechanisms. As a consequence,
both the membrane and the flexural behaviours of masonry walls have to be taken into account
for a proper estimation of the structural stability.
Macrosopic models used in structural computations are based on phenomenological laws
including a set of parameters which characterises the average behaviour of the material. These
parameters need to be identified through experimental tests, which can become costly due to
the complexity of the behaviour particularly when cracks appear. The existing macroscopic
models are consequently restricted to particular assumptions. Other models based on a detailed
mesoscopic description are used to estimate the strength of masonry and its behaviour with
failure. This is motivated by the fact that the behaviour of each constituent is a priori easier
to identify than the global structural response. These mesoscopic models can however rapidly
become unaffordable in terms of computational cost for the case of large-scale three-dimensional
structures.
In order to keep the accuracy of the mesoscopic modelling with a more affordable computa-
tional effort for large-scale structures, a multi-scale framework using computational homogeni-
sation is developed to extract the macroscopic constitutive material response from computa-
tions performed on a sample of the mesostructure, thereby allowing to bridge the gap between
macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of
quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain
largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic
homogenisation-based multi-scale approach for quasi-brittle thin shell failure.
For the numerical treatment of damage localisation at the structural scale, an embedded
strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks
using average cohesive zones including mixed cracking modes and presenting evolving orientation
related to fine-scale damage evolutions.
A first originality of this research work is the definition and analysis of a criterion based
on the homogenisation of a fine-scale modelling to detect localisation in a shell description and
determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale tran-
sition incorporating strong embedded discontinuities driven by the damaging mesostructure is
proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous ho-
mogenisation scheme is extended to a shell description in order to model the localised behaviour
of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical
masonry wall tests and verified against three-dimensional full fine-scale computations in which
all the bricks and the joints are discretised.
