Young's modulus

Young's modulus is the ratio of tensile stress to tensile strain in a material's elastic range. It quantifies resistance to elastic stretching or compression.

Stress (mechanics): Stress is internal force per unit area within a material, arising from applied loads. It is the numerator in Young's modulus: tensile stress divided by tensile strain.
Pascal (unit): The pascal is the SI unit of pressure and stress, equal to one newton per square metre. Because strain is dimensionless, Young's modulus has the same units as stress.
Beam (structure): A beam is a structural member that carries loads primarily through bending. A beam's bending deflection depends on its material's Young's modulus as well as its geometry.
Shear modulus: Shear modulus is the ratio of shear stress to shear strain in the elastic range. It measures resistance to shape change by shear, rather than axial stretching.
Strain (mechanics): Strain is the dimensionless measure of deformation, usually expressed as change in length divided by original length. It is the denominator that relates tensile stress to elastic extension.
Elastic limit: The elastic limit is the greatest stress a material can withstand without permanent deformation after unloading. The modulus applies to reversible deformation, before behavior exceeds the elastic range.
Euler–Bernoulli beam theory: Euler–Bernoulli beam theory models slender beams by relating bending and deflection while neglecting shear deformation. Its bending equations use Young's modulus to connect applied loads with beam curvature.
Bulk modulus: Bulk modulus is the ratio of pressure change to fractional volume change under compression. It measures resistance to volume change, not tensile extension.
Hooke's law: Hooke's law states that elastic deformation is proportional to applied force or stress within a material's linear range. Young's modulus is the proportionality constant linking tensile stress and strain in this range.
Tensile testing: Tensile testing measures a specimen's response as it is pulled under controlled loading. It supplies force and extension data from which stress, strain, and modulus are calculated.

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