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

The bulk modulus ($K$), Young's modulus ($E$), and Poisson's ratio ($\nu$) are related by the following equation: $K = \frac{E}{3(1-2\nu)}$

This relationship can also be rearranged to express Young's modulus in terms of bulk modulus and Poisson's ratio:

$E = 3K(1-2\nu)$

Where:

• $K$ is the Bulk Modulus (a measure of a material's resistance to uniform compression).

• $E$ is Young's Modulus (a measure of a material's stiffness or its resistance to elastic deformation under linear stress).

• $\nu$ is Poisson's Ratio (a measure of the ratio of lateral strain to axial strain).

The relationship $K = \frac{E}{3(1-2\nu)}$ is one of the fundamental equations in linear elasticity, connecting three key elastic constants.

Here is an explanation of the relationship and how it's derived from the general principles of material behavior:

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Proof and Derivation related to FAQ

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