In a context of restoration of historical masonry structures, it is crucial to properly estimatethe residual strength and the potential structural failure modes in order to assess the safety ofbuildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonrypresents preferential damage orientations, strongly localised failure modes and damage-inducedanisotropy, which are complex to incorporate in structural computations. Furthermore, masonrystructures 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 accountfor a proper estimation of the structural stability.Macrosopic models used in structural computations are based on phenomenological lawsincluding a set of parameters which characterises the average behaviour of the material. Theseparameters need to be identified through experimental tests, which can become costly due tothe complexity of the behaviour particularly when cracks appear. The existing macroscopicmodels are consequently restricted to particular assumptions. Other models based on a detailedmesoscopic description are used to estimate the strength of masonry and its behaviour withfailure. This is motivated by the fact that the behaviour of each constituent is a priori easierto identify than the global structural response. These mesoscopic models can however rapidlybecome unaffordable in terms of computational cost for the case of large-scale three-dimensionalstructures.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 betweenmacroscopic and mesoscopic representations. Coarse graining methodologies for the failure ofquasi-brittle heterogeneous materials have started to emerge for in-plane problems but remainlargely unexplored for shell descriptions. The purpose of this study is to propose a new periodichomogenisation-based multi-scale approach for quasi-brittle thin shell failure.For the numerical treatment of damage localisation at the structural scale, an embeddedstrong discontinuity approach is used to represent the collective behaviour of fine-scale cracksusing average cohesive zones including mixed cracking modes and presenting evolving orientationrelated to fine-scale damage evolutions.A first originality of this research work is the definition and analysis of a criterion basedon the homogenisation of a fine-scale modelling to detect localisation in a shell description anddetermine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale tran-sition incorporating strong embedded discontinuities driven by the damaging mesostructure isproposed 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 behaviourof out-of-plane loaded structures. These multi-scale approaches for failure are applied on typicalmasonry wall tests and verified against three-dimensional full fine-scale computations in whichall the bricks and the joints are discretised.
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