Issue 33

Y. Wang et alii, Frattura ed Integrità Strutturale, 33 (2015) 345-356; DOI: 10.3221/IGF-ESIS.33.38

After determining the direction of the maximum variance, the shear strain resolved along this direction, MV ( ) t  , can directly be evaluated, at any instant, t , of the load history, through the following relationship:

1 2

1 2 1 2

       

       





x ε (t )

(t )

(t )

xy

xz

x     y        n n n

  t



1 2

 

  

MV



(14)

q q q

γ (t ) ε (t )

yz γ (t )

xy

y

x

y

z

2

xz 1 1 γ (t ) γ (t ) ε (t ) 2 2 yz z

z

      t t t     q q q

Var

)(



        

        





 , ,





n n n



n n    n

n n    n

    

    

    

    

1



Var

)(







 , ,

k









1

n n n





Var

)(

 



1







 , ,





n n n



Figure 2 : Flowchart summarizing the algorithm for the determination of the critical plane orientation.

, and the stress normal to the plane experiencing

The shear stress resolved along the maximum variance direction, MV ( ) t 

, can be evaluated, at any instant, t , of the load history, through the

the maximum variance of resolved shear strain, n ( ) t 

following relationships:

    

x       y          z n n n

x 



 

(t ) (t ) (t )

(t ) (t ) (t )

(t ) (t ) (t )

xy

xz

  t

 

 





 

y 

q q q

(15)

x

y

z

MV

xy

yz



z 

xz

yz

349