Comptes Rendus
Bridging meso- and microscopic anisotropic unilateral damage formulations for microcracked solids
Comptes Rendus. Mécanique, Volume 345 (2017) no. 4, pp. 281-292.

A mathematically consistent and unified description of induced anisotropy and unilateral effects constitutes one of the central tasks in the continuum damage theories developed so far. This paper aims at bridging constitutive damage formulations on meso- and micro-scales with an emphasis on a complete mesoscopic determination of material effective properties for microcracked solids. The key is to introduce a new set of invariants in terms of strain tensor and fabric tensor by making use of the Walpole's tensorial base. This invariant set proves to be equivalent to the classical one, while the new one provides great conveniences to high-order orientation-dependent tensor manipulations. When limited to the case of parallel microcracks, potential relations between ten combination coefficients are established by applying continuity conditions. It is found that the dilute approximation with penny-shaped microcracks is a particular case of the present one. By originally introducing effective strain effect, interactions between microcracks are taken into account with comparison to the Mori–Tanaka method as well as the Ponte-Castaneda and Willis scheme. For completeness, discussions are also addressed on macroscopic formulations with high-order damage variables.

Published online:
DOI: 10.1016/j.crme.2017.02.003
Keywords: Continuum Damage Mechanics, Thermodynamics, Induced anisotropy, Unilateral effects, Brittle materials, Interaction between microcracks

Qi-Zhi Zhu 1; Shuang-Shuang Yuan 1; Jian-fu Shao 1, 2

1 CKey Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China
2 Laboratory of Mechanics of Lille, UMR8107 CNRS, University of Lille, Villeneuve-d'Ascq, France
     author = {Qi-Zhi Zhu and Shuang-Shuang Yuan and Jian-fu Shao},
     title = {Bridging meso- and microscopic anisotropic unilateral damage formulations for microcracked solids},
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Qi-Zhi Zhu; Shuang-Shuang Yuan; Jian-fu Shao. Bridging meso- and microscopic anisotropic unilateral damage formulations for microcracked solids. Comptes Rendus. Mécanique, Volume 345 (2017) no. 4, pp. 281-292. doi : 10.1016/j.crme.2017.02.003.

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