Issue 47

M.F. Funari et alii, Frattura ed Integrità Strutturale, 47 (2019) 277-293; DOI: 10.3221/IGF-ESIS.47.21

Without loss of generality, the following Laplace-based equations developed either in Statics (S) or Dynamics (D) are considered [23]:

  , t 

  , t 

j

j

2  

3  



  X X t    j

  X X t  j

 

 

 

1   



 

1   



0 ( ) S

0 ( ) D

(2)









,

,

2

2





t  







,

,

where j , with j =( L, R ), represents the index referred to the Left (L) or Right (R) process zones, whereas j X  corresponds to the mesh displacement function. Previous equations should be completed by boundary and initial conditions. Homogeneous conditions are required to prescribe mesh displacements at left and right ends, in such a way to verify the coincidence in terms of positional variables:     0 0, 0 0 X X          0, 0 X L X L      (3)

Figure 2 : Moving and referential coordinate systems for the skin/core interfaces.

In addition, the prescribed mesh motion at debonding length is defined by introducing a crack growth function. During the crack tip advance, the crack function is always equal to zero, whereas it is negative when the crack tip is stationary. A classical crack growth criterion, defined in terms of the Energy Release Rate (ERR) mode components normalized on the critical value, is assumed:

r

r

 

  2 G X G X   I II

   

   

2

  0 f

 

      

g X 





with

(4)

g X

1

f

G

G

IC

IIC

280