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A Transformation Field Analysis based multiscale framework for masonry structures accounting for localised failure and friction

par Mercatoris, Benoît ;Chettah, Ameur ;Massart, Thierry,Jacques
Référence International Conference on Computational Plasticity - COMPLAS(XI: September 2011: Barcelona, Spain), Proceedings of the International Conference on Computational Plasticity - COMPLAS
Publication Publié, 2011-09-05

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Résumé :

A two-scale framework combined with the semi-analytical homogenisation tool presented in [1] is presented for the failure of periodic masonry structures. 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. 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. Computational homogenisation-based multi-scale strategies are at present the most versatile approaches to take into account in a natural way evolving phenomena which take place at finer scales such as damage and plasticity. However, they remain costly in terms of computational effort for the case of large-scale structures. In order to reduce the typical high computational cost of such methods, the concept of Transformation Field Analysis (TFA) was recently extended for such materials in [1]. This approach assumes uniform inelastic strains within subdomains of a RVE by using superpositions of elastic and inelastic effects. An effective non-linear periodic homogenisation procedure combined with a micromechanical analysis of the damage process of the mortar joints is used in order to extract the structural constitutive behaviour, accounting for the coupling of the damage and friction phenomena of the mortar joints [1]. This approach only requires the off-line computational determination of transformation tensors in order to take into account the mutual interaction between evolving phases, based on eigen elastic and inelastic deformation modes of the RVE phases [1], and therefore results in efficient structural analyses.This TFA approach is here combined with embedded strong discontinuities at the structural scale in order to represent macroscopic localisation of damage and plasticity, as proposed in [2]. 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). Localisation analyses based on the acoustic tensor technique are carried to incorporate these discontinuities in a motivated manner as in [3]. For the material behaviour of the coarse-scale discontinuities, an enhanced upscaling procedure based on an approximate energy consistency recently proposed is used [4]. The results obtained with this framework will be illustrated to show that mesostructurally motivated preferential damage orientations can be naturally and efficiently incorporated into large scale computations accounting for localisation.