How to determine G12 if I have E1, E2 and v12?

No, you are using an orthotropic material model the one that you're using so you need to know it. Which type of composite are you using? Check some typical values for a similar composite and use that. Example:

Hello,

For Orthotropic materials, if you know E1, E2, and v12, you generally cannot directly calculate G12 (the in-plane shear modulus) like with isotropic materials. G12 is an independent material property and is not uniquely determined by E1, E2, and v12.

In isotropic linear elastic materials, the way the material deforms under tension (described by E), under shear (described by G), and the lateral contraction/expansion (described by v) are all manifestations of the same underlying, direction-independent material response. The material behaves the same in all directions – tension, compression, shear (not directly through E, but related to E) etc. This is not the case with orthotropic materials.

For orthotropic materials, a complete set of 9 independent properties – E1, E2, E3, G12, G13, G23 and v12, v13 and v23 must be available to fully characterize the material.

Generally, E1 / E2 ratio of 10 – 40 is typical for composites. Generally, E1 / G12 ratio is also between 10 – 40. Typically, G12 to G13 ratio is 1 and G12 to G23 is between 1.5 to 2. Note that, G23 is often lower than G12 and G13. These are generally expected, but I am not sure if they can be applied for all the Composites out there. The above predictions are for unidirectional composites and may not apply for woven composites.

Best Regards,

Vishakh.

I suspect Google would find representative values in 2 seconds.
Or see material supplier data sheets.
Or purchase a copy of CMH-17 Volume 2 at sae.org