Question

For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity $(E)$, Poisson's ratio $(\nu)$, and shear modulus $(G)$ is:

• A. $G = \dfrac{E}{2(1+\nu)}$
• B. $G = \dfrac{E}{(1+2\nu)}$
• C. $E = \dfrac{G}{2(1+\nu)}$
• D. $E = \dfrac{G}{(1+2\nu)}$

Hint:

Remember that the shear modulus is related to the Young's modulus and Poisson's ratio for isotropic materials using the formula \( G = \dfrac{E}{2(1+\nu)} \).

Answer 1

The Correct Option is A

For a linear elastic and isotropic material, the correct relationship between Young's modulus \(E\), Poisson's ratio \(\nu\), and shear modulus \(G\) is: \[ G = \dfrac{E}{2(1+\nu)} \] This relationship is derived from the equations that relate stress, strain, and material properties for isotropic materials. The correct option is (A).