I did another trick: Increasing G_c has the same effect to achieve purely 
elastic behavior. So, I chose a high enough G_c value and it works!
I obtain the same results and the duh values grow correctly. 

Still I cannot understand fully why when cracking is initiated, there is no 
increase of the strains except the strain in the loaded direction.
Maybe you are right, I try to compare a bigger example, but I already 
compared two phase-field codes.
I have my own version with staggered scheme and it was not identical to 
your results after crack initiation.
As mentioned before, in the elastic regime everything is identical and fine.

The only thing I changed a bit is the integration from quadratic to linear, 
but I am not sure, if seeting quadrature_formula(2) alone is enough for 
linear shape functions. You also had face_quadrature_formula or this 
Lobatto integration.
Would you be so kind and explain what lines I have to change in order to 
obtain linear shape functions and not quadratic like set in the original 
version?
How many changes and the code would help a lot.
Just to be sure I did it correct.

Thank you.

Best,
Seyed Ali 

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