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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
Author(s) -
Mercatoris B. C. N.,
Massart T. J.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3018
Subject(s) - dissipation , homogenization (climate) , masonry , classification of discontinuities , brittleness , planar , structural engineering , material failure theory , shell (structure) , anisotropy , microscale chemistry , scale (ratio) , failure mode and effects analysis , materials science , mechanics , statistical physics , computer science , physics , engineering , finite element method , mathematics , composite material , mathematical analysis , biodiversity , quantum mechanics , biology , mathematics education , ecology , computer graphics (images) , thermodynamics
This 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. Copyright © 2010 John Wiley & Sons, Ltd.