Glossary term
Young's Modulus
The elastic modulus relating uniaxial stress to uniaxial strain in the linear elastic range.
Definition
quantityYoung's modulus is the ratio of uniaxial stress to uniaxial strain in the linear elastic range of a material.
Young's modulus describes axial stiffness rather than strength. It is used to predict elastic deformation, vibration, buckling, contact compliance, wave speed, and finite-element response, but its value depends on material structure, temperature, loading direction, strain range, rate effects, and whether the material behaves linearly.
Young’s modulus is the slope of the linear elastic portion of a uniaxial stress-strain curve:
where sigma is normal stress and epsilon is normal strain. A high value of E means the material strains less under the same axial stress. It does not mean the material has high yield strength, high toughness, or high fatigue resistance.
Engineering use
Young’s modulus is used in beam deflection, axial stiffness, buckling, vibration, finite-element analysis, pressure-vessel deformation, machine compliance, civil structures, composites, and material comparison. For isotropic linear elastic materials, it is linked to shear modulus and Poisson’s ratio. For anisotropic materials, different moduli may apply in different directions.
Measurement can come from tensile tests, compression tests, bending tests, resonant methods, ultrasonic methods, or supplier data. The measured value can change with strain range, temperature, loading rate, porosity, moisture, damage, fiber orientation, heat treatment, and microstructure. Polymers, rubbers, foams, composites, and biological materials may not have one constant modulus over the working range.
Common mistakes
A common mistake is using Young’s modulus as a strength property. It predicts elastic deformation, not the stress at which yielding or fracture occurs. Another mistake is taking a tangent modulus, secant modulus, dynamic modulus, and static tensile modulus as interchangeable. A strong material model states the modulus definition, test method, strain range, direction, temperature, rate, moisture or aging condition, and whether linear elasticity is assumed.