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Hooke's Law provides us the relation for uniaxial stress |
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The constant of proportionality is called the elastic modulus , modulus of elasticity or Young's modulus . Since  is dimensionless the unit of E is same as that of uniaxial stress (e.g.  ). |
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Uniaxial forces case strains not only in its direction, but also in the transverse/lateral directions. For a tensile strain in the axial direction, there will always be compressive strains in the lateral directions, and vice versa. Poisson's Ratio (  ) relates the lateral strains to the axial strain
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Note that this ratio is always a dimensionless positive number.
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1.3.3 |
Coefficient of Linear Thermal Expansion |
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 has units of per degrees Centigrade (or Fahrenheit) |
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For shear stress (  ) and shear strain (  ), we have a constitutive relation similar to the Hooke's Law for linear stress and strain. |
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The constant of proportionality ( G ) is known as the shear modulus or modulus of rigidity . It has same units as modulus of elasticity ( E ). It can be proved that: |
1.3.5 |
Dilatation and Bulk Modulus |
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Dilatation ( e ) is defined as the change of volume per unit volume |
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If a three-dimensional body is subjected to uniform hydrostatic pressure p , then the ratio of this (compressive) pressure to the dilatation is known as the bulk modulus ( k ) |
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k is also called the modulus of compression .
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) due to change in temperature ( 
) is obtained by using this coefficient ( 
) 
