# Young's modulus

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Young's Modulus, or lambda E, is an elastic modulus is a measure of the stiffness of a material. It is used extensively in quantitative seismic interpretation, rock physics, and rock mechanics. It is defined as the ratio of uniaxial stress to uniaxial strain when linear elasticity applies. It is analogous to the proportionality constant in Hooke's Law ${\displaystyle F=-kx}$.

## In terms of VP and VS

${\displaystyle E={\frac {1}{2}}}$

## Other expressions

λ can also be expressed in terms of Young's modulus, E, and Poisson's ratio, ν:

${\displaystyle \lambda ={\frac {E\nu }{(1+\nu )(1-2\nu )}}}$

The simplest expression casts λ in terms of bulk modulus and shear modulus μ:

${\displaystyle \lambda =K-{\frac {2}{3}}\mu }$