YoungModulus

Young's modulus, denoted E, is the ratio of tensile stress to the corresponding linear elastic strain in a material under uniaxial loading. In Hooke's law, sigma = E * epsilon for small strains within the elastic region. The quantity is a measure of stiffness; higher E means a stiffer material. The units are pascals (Pa); common values are given in gigapascals (GPa).

Typical values vary widely by material. Steel is about 190–210 GPa, aluminum around 70 GPa, and glass roughly 60–70 GPa. Concrete is in the 20–40 GPa range, while polymers span a broad range and rubber can be very low, around 0.01–0.1 GPa. E can also depend on temperature, loading rate, and, in anisotropic materials, crystallographic direction or material orientation.

Relationships with other elastic moduli are often used to relate stiffness measures. For isotropic materials, E is related to the shear modulus G and Poisson's ratio ν by E = 2G(1+ν). Another common relation is E = 9KG/(3K+G), where K is the bulk modulus. In anisotropic materials such as crystals and composites, E can vary with direction; in composites, the effective E along the fiber direction can be much higher than in other directions.

Measurement methods include tensile tests that yield a stress–strain curve and determine the slope of the linear region, and ultrasonic or resonance methods for nondestructive assessment. E is widely used in engineering design to predict deflection, natural frequency, and load-bearing capacity, with the caveat that it describes linear elastic behavior and can change with temperature and strain rate.