Issue 58

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

This strain is a consequence of opening the cracks too large. This fracture strain of the inclusions is limited as follows:

  = rt ft

(50)

The damage is progressive in the field of strains. For a uni-axial state of tension, the equivalent strain ( ) ( )    1 2 , t t D D , in the nonlinear field is such that:

 





( )   → = =         → = =  ft u 1 u r 2 t t D D ( )         

=

( ) ( E E D D 1- 1-

)

ct

t

1

t

1

(51)





=

(

) (

)

1- E E D D 1

ct

t

2

t

2

and

( f , 

) ( )  =





 

D D

-

0

t

1

t

1 ft

( ) 1 t D







    → r

(52)

ft

( f , 

) ( )  =





D D

-

0



t

2

t

2 r

Figure 6: Damage model algorithm implementation diagram.

The threshold function defines two limit states: - An elastic state ( )  ft . - A breaking limit given by the value ( )  r . Such as:

 

→

D

=0

 = 

ft

t

1

( f , 

)

= →  0

D

(53)

t

1

 =





→

D

=0



r

t

2

330