Issue 52

M.F. Bouali et alii, Frattura ed Integrità Strutturale, 52 (2020) 82-97; DOI: 10.3221/IGF-ESIS.52.07

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)

E E

m g



E

Reuss model  10, 19  :

(2)





c_ Reuss

g g m g E V E E  

1 2





Voigt E E 

Reuss

Popovics model  10, 20  :



. (3)

E

c_ Popovics

c

c

1

1



E

Hirsch-Dougill model  10, 15, 21  :

(4)

c_ Hirsch

2 1 

   

1



  

E

E

c_ Voigt

c_ Reuss

      E E E E V               m g E E E E V g m g m g g m g

Hashin-Hansen model  10, 11, 22  :



.

(5)

E

E

c_ Hashin

m





   1 2V α 1 / α 2 1 V α 1 / α 2 E E            g g g



      

   

   



E

E



c_ Maxwell

m

Maxwell model (dispersed phase)  10, 15  :

.

(6)

m

     

      

V

g

 

Counto1 mod  17, 23  :

E

m E 1

. (7)

c_Counto1

E

 

m

V V





g

g

E E 

g

m

     

      

V

g

 

Counto2 model  17  :

E

m E 1

.

(8)

c_Counto2

E

g



V





g

E E 

g

m

V

m E E   V

Bache and Nepper-Christensen model  15, 24  :

E

(9)

g

c_ Bache

m

g

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