Mode II strain energy release rate

Hello guys,

I have a silly question. We all know that mode II strain energy release rate was given as GII=KII^2/E for linear elastic material. My question is why E (Young's modulus) but not G (shear modulus) appears in the equation, because Mode II crack propagation is attributed to the shear stress. On the other hand, it seems self-explanatory that we use E for mode I and G for Mode III.

I just wonder if there is a simple explanation to that.

Gan