❓How is the shear modulus related to Young's modulus and Poisson's ratio?

The shear modulus ($G$) is related to Young's modulus ($E$) and Poisson's ratio ($\nu$) by the following equation: $G = \frac{E}{2(1 + \nu)}$ . This relationship is a fundamental one in the theory of linear elasticity, connecting the modulus that describes a material's resistance to shear deformation ($G$) with the modulus describing its resistance to axial deformation ($E$) and its lateral contraction properties ($\nu$).

This relationship is a core equation in the field of linear elasticity for isotropic (having the same properties in all directions) and homogeneous materials.

Explanation of the Constants

1. Shear Modulus ($G$): Also known as the Modulus of Rigidity.

   • What it measures: The material's resistance to shearing or twisting—a change in shape without a change in volume. It's the ratio of shear stress to shear strain.

2. Young's Modulus ($E$):

   • What it measures: The material's stiffness or resistance to axial (tensile or compressive) stress—a change in length. It's the ratio of axial stress to axial strain.

3. Poisson's Ratio ($\nu$):

   • What it measures: The material's tendency to contract laterally when stretched axially. It's the ratio of lateral strain (change in width) to axial strain (change in length).

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How is the shear modulus related to Young's modulus and Poisson's ratio? | FAQsviadean on Notion