Young Modulus

The Young modulus is the single most important quantity for describing the stiffness of a material. Named after Thomas Young, who formalised the concept in the early 19th century, it tells you how much a material resists elastic deformation under stress.

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Defining Young Modulus

The Young modulus (E) is defined as the ratio of stress to strain in the linear (elastic) region:

$E = \frac{\sigma}{\varepsilon} = \frac{F/A}{\Delta L / L} = \frac{FL}{A \Delta L}$E=εσ​=ΔL/LF/A​=AΔLFL​

where:

• E is the Young modulus in Pa (or more commonly GPa)
• F is the applied force in N
• A is the cross-sectional area in m²
• L is the original length in m
• ΔL is the extension in m

The Young modulus has units of pressure (Pa) because strain is dimensionless, so E has the same units as stress.

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Interpreting the Young Modulus

A large Young modulus means the material is stiff — it resists deformation. A small Young modulus means the material is flexible — it deforms easily under stress.