# Shear modulus in terms of 2 Young's moduli and Poisson ratio

I have two moduli, EY and EZ, and the poisson ratio NUYZ, and the equation for the shear modulus that I am using is

$$G = \frac{EY*EZ}{EY+EZ+2*EY*NUYZ}$$ but I am not sure where it comes from.

I tried seeing if I could somehow rearrange the shear modulus from wikipedia: $$G = \frac{E}{2(1+\nu)}$$ but did not have any luck, so I was wondering if there was something obvious I am missing. Apologies if this is an easy problem, I am new to shears/Young's moduli, but if anyone could explain where my equation comes from it would be super helpful! Thank you!

• For an anisotropic material the notion of "shear modulus" is not so useful, since a circular cross section bar will not stay circular in torsion. Your formula is obviously the same as the isotropic material formula if EY = EZ. Sep 14 '20 at 23:39
• Mikeb did you find an answer to your question? Could you share it? Jul 20 at 15:24