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ELASTIC CONSTANTS



Introduction
In material science, it is necessary to have a quantity in terms of value to measure the response of a material to a particular type of deformation (either elastic or inelastic in nature) under the action of a stress or load. These number values are called as elastic constants. We will deal with the different types of elastic constants associated with a material and their interdependencies.

Two independent quantities are only required in order to completely define the properties of a material say whether it is isotropic, elastic medium. And we have many constants available from which the two of them can be determined. These constants are originated as a value of proportionality between stress and strain under different loading conditions.

Definition of constants
The available constants are:
  • · Modulus of elasticity or Young's Modulus
  • · Modulus of rigidity or shear modulus of elasticity
  • · Bulk modulus or Volume modulus of elasticity
  • · Poisson's Ratio
 Each of the constants is explained below with their values for different materials. Note: Hooke's Law states that a material that is loaded within the elastic limit have the stress directly proportional to the strain produced. This means the ratio of stress to strain is equal to a constant within the elastic limit.

Modulus of elasticity (E)
It is defined as the ratio between stress and strain associated with a material. The stress caused may be either compressive or tensile in nature. Its unit is kN/m2.


 Modulus of Rigidity or Shear Modulus
It is defined as the ratio of shear stress to shear strain within the elastic limit. It is represented as C or G



Bulk Modulus
A body subjected to direct stresses equally in mutually perpendicular direction would create a volumetric strain, which is found to be constant within the elastic limit for a given material. It is usually represented by K .



Poisson's Ratio
The Poisson's ratio is defined as the ratio of lateral strain to the longitudinal strain for a given material, within the elastic limit. It is represented by μ.



As strain produced in the lateral direction is opposite in direction to the longitudinal stress a negative sign is used.

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