In solid mechanics, Young's modulus or modulus of elasticity (and also elastic modulus) is a measure of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. This can be experimentally determined from the slope of a stress-strain curve created during tensile test s conducted on a sample of the material.

Contents

1 Units 2 Other units 3 Usage 3.1 Linear vs Non-linear 4 Calculation 4.1 Tension 4.2 Elastic potential energy 5 Approximate values 6 See also

Units

The SI unit of modulus of elasticity is the Pascal.

Other units

The modulus of elasticity can also be measured in other units of pressure, for example pounds per square inch (psi).

Usage

The Young's modulus allows the behavior of a material under load to be calculated. For instance, it can be used to predict the amount a wire will extend under tension, or to predict the load at which a thin column will buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus , density or Poisson's ratio.

Linear vs Non-linear

For many materials, Young's modulus is a constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials include steel, carbon fiber and glass. Rubber is a non-linear material.

Calculation

The modulus of elasticity, λ, can be calculated by dividing the stress by the strain, i.e.

where

λ is the modulus of elasticity, measured in pascals

F is the force, measured in newtons

A is the cross-sectional area through which the force is applied, measured in square metres

x is the extension, measured in metres

l is the natural length, measured in metres

Tension

The modulus of elasticity of a material can be used to calculate the tension force it exerts under a specific extension.

where

T is the tension, measured in newtons

Elastic potential energy

The elastic potential energy stored is given by the integral of this expression with respect to x, i.e. energy stored E is given by:

where

E is the elastic potential energy, measured in joules

Approximate values

Approximate Young's Moduli of Various Solids

Material	Young's modulus (E) in MPa	Young's modulus (E) in PSI	Young's modulus (E) in [GPa] (source cornell university)
Soft cuticle of pregnant locust	0.21	30
Rubber (small strain)	6.9	1000
Shell membrane of egg	7.58	1100
Human cartilage	24.13	3500
Human tendon	551.6	80,000
Wallboard	1,379	200,000
Unreinforced plastics, polyethene, nylon	1,379	200,000
Plywood	6,895	1,000,000
Wood (along grain)	6,895	1,000,000
Fresh bone	20,685	3,000,000
Magnesium metal	41,370	6,000,000
Ordinary glasses	68,950	10,000,000
Aluminium alloys	68,950	10,000,000
Brasses and bronzes	117,215	17,000,000	103 - 124
Titanium (Ti)			116
Iron and steel	206,850	30,000,000
Beryllium (Be)			200 - 289
Aluminium oxide (Al2O3) (Sapphire)	413,700	60,000,000	390
Tungsten carbide (WC)			450 -650
Silicon carbide (SiC)			450
Diamond (C)	1,172,150	170,000,000	1000

See also

• Deformation
• Stress
• Strain