Young’s Modulus

Young’s modulus is a material property that measures a material’s stiffness—its ability to resist deformation under tensile or compressive stress. It quantifies the relationship between stress and strain in the elastic region of a material’s stress-strain curve (it is the slope of the linear part of the curve), where deformation is reversible. The formula for Young’s modulus is:

Young’s modulus = stress / strain or E = σ / ε,

where E is Young’s modulus, σ (sigma) is stress, and ε (epsilon) is strain. Since strain is dimensionless (a ratio of length change to original length), the units of Young’s modulus are the same as stress:

  • SI units: Pascals (Pa), typically expressed in gigapascals (GPa) because most materials have large values of E.
  • U.S. Customary units: Pounds per square inch (psi) or kilopounds per square inch (ksi).

Young’s modulus is a critical property in structural and mechanical design because it helps engineers predict how much a material will stretch or compress under load. A higher Young’s modulus indicates a stiffer material, while a lower Young’s modulus indicates a more flexible material.

The steel bar (rear) has a higher Young’s modulus than the aluminum bar (front). Both bars are the same size and shape and are constrained and loaded identically.

Because Young’s modulus only applies to the elastic region, it does not predict permanent deformation or failure. It is primarily used to assess material behavior under normal operating conditions where elasticity is maintained.

Other Moduli of Elasticity

There is a subtle but meaningful distinction between Young’s modulus and the modulus of elasticity, though they are often used interchangeably in many engineering contexts. Young’s modulus (E) specifically refers to the modulus of elasticity in uniaxial tension or compression, meaning it describes how a material resists stretching or compressing in a linear elastic manner....

Other Moduli of Elasticity

There is a subtle but meaningful distinction between Young’s modulus and the modulus of elasticity ,...