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SUMMARYThis paper presents a multi-scale framework for the failure of periodic quasi-brittle thin planar shells. The failure behavior of textured or periodic heterogeneous materials is strongly influenced by their mesostructure. Their periodicity and the quasi-brittle nature of their constituents result in complex behaviors such as damage-induced anisotropy properties with localization of damage, which are difficult to model by means of macroscopic closed-form constitutive laws. A computational homogenization procedure is used for the in-plane and out-of-plane behavior of such planar shells, and is combined with an acoustic tensor-based failure detection adapted to shell kinematics to detect the structural-scale failure. Based on an assumption of single period failure, the localization of damage at the structural scale is represented by means of mesostructurally informed embedded strong discontinuities incorporated in the macroscopic shell description. A new enhanced scale transition is outlined for shell failure, based on an approximate energy consistency argument to objectively upscale the energy dissipation. The corresponding multi-scale framework results are compared with direct fine-scale modeling results used as a reference for the case of masonry, showing good agreement in terms of the load-bearing capacity, of failure mechanisms and of associated energy dissipation.

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