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A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry

par Mercatoris, Benoît ;Massart, Thierry,Jacques
Référence International Conference on Computational Modelling of Fracture and Failure of Materials and Structures - CFRAC(II: June 2011: Barcelona, Spain), Proceedings of the International Conference on Computational Modelling of Fracture and Failure of Materials and Structures - CFRAC
Publication Publié, 2011-06-30

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Résumé :

A coupled two-scale framework is presented for the failure of periodic masonry shell structures, in which membrane-flexural couplings appear. The failure behaviour of textured heterogeneous materials such as masonry is strongly influenced by their mesostructure. Their periodicity and the quasi-brittle nature of their constituents result in complex behaviours such as damage-induced anisotropy properties with localisation of damage, which are difficult to model by means of macroscopic closed-form constitutive laws. The multi-scale computational strategies aim at solving this issue by deducing a homogenised response at the structural scale from a representative volume element (RVE), based on constituents properties and averaging theorems. The constituents inside the RVE may be modelled using any closed-form formulation, depending on the physics to represent. Scale transitions for homogenisation towards a Kirchhoff-Love shell behaviour were recently proposed. The microstructure is represented by a unit cell on which a strain-periodic displacement field is imposed. The localisation of damage at the structural scale is represented by means of embedded strong discontinuities incorporated in the shell description. Based on an assumption of single period failure, the behaviour of these discontinuities is extracted from further damaging RVEs, denoted as localising volume elements (LVEs). An acoustic tensor-based criterion adapted to shell kinematics is used to detect the structural-scale failure and find its orientation. For the material behaviour of the coarse-scale discontinuities, an enhanced upscaling procedure based on an approximate energy consistency has been proposed recently for the in-plane case and is extended to the out-of-plane case. Such a multi-scale scheme can be implemented using parallel computation tools. The corresponding multi-scale simulation results are compared to direct fine-scale computations used as a reference for the case of masonry, showing a good agreement in terms of load bearing capacity, of failure mechanisms and of associated energy dissipation.