Youngsmodulus

Young's modulus, denoted E, is a measure of the stiffness of a solid material. It is defined as the ratio of tensile stress to tensile strain in the linear portion of the stress–strain curve, i.e., E = σ/ε, where σ is stress and ε is strain. This definition applies to the elastic region before plastic deformation. E is expressed in pascals (Pa) or gigapascals (GPa). For isotropic, homogeneous materials, E is a single constant; for anisotropic materials such as composites or crystals, the value depends on the loading direction.

Measurement typically involves a tensile (or compression) test, from which the slope of the initial straight portion of the stress–strain curve yields E. Other methods include resonant frequency tests or ultrasonic elasticity measurements.

Typical values vary widely. Steel has about 200 GPa, aluminum around 69 GPa, tungsten about 400 GPa, and glass around 50–70 GPa. Polymers range from roughly 0.1 to a few GPa, with rubbery polymers much lower. In composite materials, the modulus can be very high along preferred fiber directions (often 100–200 GPa), but much lower in transverse directions.

Applications: Young's modulus is foundational in structural design and mechanical analysis, used in calculations of deflections, stresses, and stability. Temperature, manufacturing, and material direction can alter E; in polymers, E typically decreases with temperature. E, together with other elastic constants such as shear modulus G, bulk modulus K, and Poisson's ratio ν, describes elastic behavior of materials, with isotropic relation E = 2G(1+ν).