Issue 58

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

( )  eq f= -K D =0

(39)

with:

( )  eq K D =

if

D=0

(40)

Figure 4: Behavior of concrete according to the Mazars model ([29], [30]).

The relation between these variables is given as follows:

    t t c c D= D + D

(41)

Usually the value of  is fixed at 1.06. The coefficients  t and  c carry out a link between the damage, and the state of traction or compression. When traction is activated  = t 1 while  = c 0 , and vice-versa in compression. The damage evolution laws t D and c D are expressed only from the equivalent strain  eq .

(

)

1-A

(

)

(

)

t

 

(42)

D =1-

-A exp -B -

t

t

t

eq d0



eq

(

)

1-A

(

)

(

)

c

  c eq d0

(43)

D =1-

-A exp -B -

c

c



eq

with:  d0 : The threshold strain of damage,  : Coefficient which was introduced later to improve the shear behavior,

B and : Material parameters to identify.

t c t A , A , B ,

c

Damage model from Bouafia et al. To describe the behavior of composites with cylindrical inclusions in tension. The relationships proposed by Bouafia et al. ([31], [32]) within the framework of the theory of beams, with taking into account of the damage which was developed for

328