Issue 58

K. Benyahi et alii, Frattura ed Integrità Strutturale, 58 (2021) 319-343; DOI: 10.3221/IGF-ESIS.58.24

the behavior of the concrete of fibers in tension (Fig. 5). The fibers (cylindrical inclusions) are dispersed in the concrete at random, and the modeling is carried out considering a uniform distribution.

Figure 5 : Constitutive law (σ - ε) in traction of steel fiber concrete [ 31].

The variable of the damage in uni-axial traction, is given by:

6

(

) (

        

   

   

)



−

  -

f



uc

ft

u

uc

( ) 

     → = − 1 D

-

ft

u

t

1

6

(

) (

 t

)

E E

 t

  ft u -

ct

ct

(44)

6



   

(

)

  -



u

uc

( ) 

    → = − 1 D 

− 

. 1

u

r

t

2

6

 t

(

)

E





-

 

ct



r u

The maximum ultimate stress of the composite (function of the characteristics of inclusions):

   l

0

f

u



= c

(45)

u



The reference length is linked to the height h of the section:

 = h r l

(46)

The initial modulus of the composite in traction is given by:

(

)   +

0 = 1 ct b E n E

(47)

0

The ultimate strain corresponding to the total mobilization of the inclusions-matrix adhesion, is given by:

2

 l E h   u f





+

=

(48)

u

ft

3

f

When there is tearing of inclusions, the breaking strain of the composite, is given by:

2



l

l

u f

f

  =

+

+

(49)

rt

ft

   4 h

3

E h

f

329