In solid mechanics, Young's modulus (E) is a measure of the stiffness of an isotropic elastic material. It is also known as the Young modulus, modulus of elasticity, elastic modulus (though Young's modulus is actually one of several elastic moduli such as the bulk modulus and the shear modulus) or tensile modulus. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds.^{[1]} This can be experimentally determined from the slope of a stressstrain curve created during tensile tests conducted on a sample of the material.
Young's modulus is named after Thomas Young, the 19th century British scientist. However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young's modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782 — predating Young's work by 25 years.^{[2]}
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Young's modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore Young's modulus itself has units of pressure.
The SI unit of modulus of elasticity (E, or less commonly Y) is the pascal (Pa or N/m²); the practical units are megapascals (MPa or N/mm²) or gigapascals (GPa or kN/mm²). In United States customary units, it is expressed as pounds (force) per square inch (psi).
The Young's modulus allows the behavior of a bar made of an isotropic elastic material to be calculated under tensile or compressive loads. For instance, it can be used to predict the amount a wire will extend under tension or buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson's ratio.
For many materials, Young's modulus is essentially 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 and soils (except at very small strains) are nonlinear materials.
Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic: Their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic, and Young's modulus will change depending on the direction from which the force is applied. Anisotropy can be seen in many composites as well. For example, carbon fiber has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating structures.
Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain:
where
The Young's modulus of a material can be used to calculate the force it exerts under a specific strain.
where F is the force exerted by the material when compressed or stretched by ΔL.
Hooke's law can be derived from this formula, which describes the stiffness of an ideal spring:
where
The elastic potential energy stored is given by the integral of this expression with respect to L:
where U_{e} is the elastic potential energy.
The elastic potential energy per unit volume is given by:
This formula can also be expressed as the integral of Hooke's law:
For homogeneous isotropic materials simple relations exist between elastic constants (Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio ν) that allow calculating them all as long as two are known:
Young's modulus can vary somewhat due to differences in sample composition and test method. The rate of deformation has the greatest impact on the data collected, especially in polymers. The values here are approximate and only meant for relative comparisons.
Material  GPa  lbf/in² (psi) 

Rubber (small strain)  0.010.1  1,50015,000 
ZnO NWs^{[citation needed]}  2137  3,045,7925,366,396 
PTFE (Teflon)^{[citation needed]}  0.5  75,000 
Low density polyethylene^{[citation needed]}  0.2  30,000 
HDPE  0.8  
Polypropylene  1.52  217,000290,000 
Bacteriophage capsids^{[4]}  13  150,000435,000 
Polyethylene terephthalate  22.7  
Polystyrene  33.5  435,000505,000 
Nylon  24  290,000580,000 
Diatom frustules (largely silicic acid)^{[5]}  0.352.77  50,000400,000 
Mediumdensity fibreboard^{[6]}  4  580,000 
Pine wood (along grain)^{[citation needed]}  8.963  1,300,000 
Oak wood (along grain)  11  1,600,000 
Highstrength concrete (under compression)  30  4,350,000 
Magnesium metal (Mg)  45  6,500,000 
Aluminium  69  10,000,000 
Glass (see chart)  5090  
Kevlar^{[7]}  70.5112.4  
Motherofpearl (nacre, largely calcium carbonate) ^{[8]}  70  10,000,000 
Tooth enamel (largely calcium phosphate)^{[9]}  83  12,000,000 
Brass and bronze  100125  17,000,000 
Titanium (Ti)  16,000,000  
Titanium alloys  105120  15,000,00017,500,000 
Copper (Cu)  117  17,000,000 
Glass fiber reinforced plastic (70/30 by weight fibre/matrix, unidirectional, along grain)^{[citation needed]}  4045  5,800,0006,500,000 
Carbon fiber reinforced plastic (50/50 fibre/matrix, unidirectional, along grain)^{[citation needed]}  125150  18,000,00022,000,000 
Wrought iron  190–210  
Steel  200  29,000,000 
polycrystalline Yttrium iron garnet (YIG)^{[10]}  193  28,000,000 
singlecrystal Yttrium iron garnet (YIG)^{[11]}  200  30,000,000 
Beryllium (Be)  287  42,000,000 
Tungsten (W)  400410  58,000,00059,500,000 
Sapphire (Al_{2}O_{3}) along Caxis^{[citation needed]}  435  63,000,000 
Silicon carbide (SiC)  450  65,000,000 
Osmium (Os)  550  79,800,000 
Tungsten carbide (WC)  450650  65,000,00094,000,000 
Singlewalled carbon nanotube^{[12]}  1,000+  145,000,000+ 
Diamond (C)^{[13]}  1220  150,000,000175,000,000 


Conversion formulas  

Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.  
Contents 
For Thomas Young, English scientist.
Young's modulus (plural Young's moduli)


