Multi-scale detection of failure in planar masonry thin shells using computational homogenisation

This paper presents a computational homogenisation-based technique for localisation detection in planar masonry shells. A computational homogenisation procedure is used for the in-plane and the out-of-plane behaviour of masonry walls taking the periodicity of the material into account. The quasi-brittle nature of the masonry constituents results in initial and damage-induced (evolving) anisotropy properties with localisation of damage at both the structural and fine scales. Using a closed-form damage model at the mesoscopic scale, it is shown that a structural scale localisation criterion based on the acoustic tensor adapted to shell kinematics allows to detect the structural scale localisation. This detection identifies average preferential cracking orientations consistent with the stacking mode of masonry for both in-plane and out-of-plane failure. This approach is illustrated by examples of bed joint and stair-case failure, and its subsequent integration in multi-scale nested computational schemes is discussed.