Issue 39

M. A. Lepore et alii, Frattura ed Integrità Strutturale, 39 (2017) 191-201; DOI: 10.3221/IGF-ESIS.39.19



 n n n n n n 0 0 ,   ,   0     





D K K

1

0

  

(6)





 1 

 s s 

 

(7)

D K 0

where D is the damage function and the initial stiffness K n0

and K s0

are the slope of the first segment of mode I and mode

II cohesive curve, respectively. The structure of the algorithm requires the displacement jump u and its relative increments d u as data input, whilst provides as output with  ,  and its derivative respect to the displacement jump components. For each integration step, the value of displacement jump across the interface  n is compared with the state variable  max , which is associated with the current damage (5), reported here:

     





t 0,  max  

max

 

where t is the variable time. When separation is greater than previous  max

  n 

f  

, i.e. the point (  curr

,  curr

) is located on the effective limit curve

(Fig. 4), the damage D is increasing according to the relationship

ncurr n KD K 0

1  

(8)

Being curr 

equal to the updated max 

, the current stiffness is



 max



f



 

K

(9)

ncurr

n 



max

whilst the initial stiffness   n K f 0 0  

(10)

Then, the stress field is recalculated according to Eqs. (6)-(7).



f (  curr

) 

P i 

P 2 

P 1 

K curr



P n 

( t )   curr

( t ) 

 max

 n



Figure 4 : Interpolated cohesive law – opening of the interface.

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