YoungsModul

Youngsmodul, commonly called Young's modulus, is a measure of the stiffness of a solid material. It describes how much stress is required to produce a given amount of strain in the elastic, uniaxial region of the stress–strain curve. Mathematically, it is defined as E = σ/ε, where σ is tensile stress and ε is axial strain. The term is named after Thomas Young, a 19th‑century British physicist.

For isotropic materials, Young's modulus is a single scalar quantity that characterizes stiffness in any direction. Its values vary widely between materials: metals such as steel are around two hundred gigapascals, aluminum is about sixty to seventy gigapascals, ceramics often exceed tens to hundreds of gigapascals, and polymers typically lie in the low gigapascal range. In anisotropic materials, such as fiber-reinforced composites, E can differ by direction and is specified as E along a principal axis.

Young's modulus is related to other elastic constants. It can be expressed as E = 2G(1 + ν), linking it to the shear modulus G and Poisson's ratio ν, and as E = 3K(1 − 2ν), linking it to the bulk modulus K. Measurement methods include standard tensile tests, resonant-frequency methods for dynamic stiffness, and indentation techniques for small-scale samples.

Applications and limitations: E indicates stiffness but not strength or ductility. It generally decreases with increasing temperature and can vary with processing, moisture, and orientation in composites. In engineering design, E is used to predict deflection and vibration responses, such as beam bending and natural frequencies, where stiffer materials resist deformation more effectively.