Issue 52

M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07 84 As explained by Gilormini and Brechert  18  , the choice of a model is governed by several parameters including the geometry of the heterogonous medium, the mechanical contrast between the phases (E g /E m ) and the volume fraction of reinforcement (V g ). Therefore, the equivalent homogenous behavior of LWAC depends of the characteristics of the mortar (matrix, phase m) and lightweight aggregate (dispersed phase, phase g). Figure 1: Composite models: (a) Voigt model, (b) Reuss model, (c) Popovics model, (d) Hirsch-Dougill model, (e) Hashin-Hansen model, (f) Maxwell model, (g) Counto1 model, (h) Counto2 model. Voigt model  10, 19  : c_ Voigt m m g g E E V E V   . (1) Reuss model  10, 19  :   m g c_ Reuss g g m g E E E E V E E    (2) Popovics model  10, 20  :   Voigt Reuss c_ Popovics c c 1 E E E 2   . (3) Hirsch-Dougill model  10, 15, 21  : c_ Hirsch c_ Voigt c_ Reuss 1 1 E 2 1 1 E E           (4) Hashin-Hansen model  10, 11, 22  :         m g g m g c_ Hashin m m g g m g E E E E V E E E E E E V                . (5) Maxwell model (dispersed phase)  10, 15  :         g c_ Maxwell m g g m 1 2V α 1 / α 2 E E 1 V α 1 / α 2 E E                         . (6) Counto1 mod  17, 23  :   g c_Counto1 m m g g g m V E E 1 E V V E E                   . (7) Counto2 model  17  :   g c_Counto2 m g g g m V E E 1 E V E E                  . (8) Bache and Nepper-Christensen model  15, 24  : g m V V c_ Bache m g E E E   (9)