For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity (E), Poisson’s ratio (ν), and shear modulus (G) is

1
\(\rm G = \frac{E}{2(1 + \nu)}\)
2
\(\rm G = \frac{E}{(1 + 2\nu)}\)
3
\(\rm E = \frac{G}{2(1 + \nu)}\)
4
\(\rm E = \frac{G}{(1 + 2\nu)}\)

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