Issue 42

M. Olzak et alii, Frattura ed Integrità Strutturale, 42 (2017) 46-55; DOI: 10.3221/IGF-ESIS.42.06



p p s s  

p

p

3

3

i 1 i i 1 i    s

i 1 

i i



h

h

1 2

1

s





i

i

Δh

i 1 

i

2 12  

(2)

s   i 1 i 1 2

s

Δt

where:

h i 1 i  

 

h

h h i

i 1



h 1 i

h 1 i

;

;





2

2

2

2

Δh i v i Δt 

After transformation and substitution for

being the velocity of crack faces motion we have

3

3

3

3

     

     

h

h

h

h

1 2

1 2

1 2

1 2









i

i

i

i







p  



p   i 1 

    



p

6 η v s

s

(3)

i 1 

i 1 i 1  

i

i

s s 



s s 



s

s

s

s

i 1 

i 1 i 

i 1 

i 1 i 

i

i

The discrete boundary conditions have the form p 1 = p amb p n = p n-1 After writing Eq (3) for all sections of the crack we obtain the following set of linear equations with a 3-diagonal matrix

p

          

          

B A

D 1 D 2  

          

          

          

1 1

1 2

p

C B A 2 2 2

       

 



 

 

 



(4)



C B A n 1 n 1 n 1   

D p n 1  

  

n 1

C B

D

n

n

n

p n

where:

3 A h i 1 i 2  3 C h i 1 i 2 







 

3

3

B h   



h

i

1 2

1 2

i        i



D 6 η v s i i 1 i 1        and from the boundary conditions we have s i

50