One of the most essential qualities of solid materials is the elastic modulus, which is a material parameter that describes stiffness. When deformation is completely elastic, it is the ratio of stress to strain. Strain is defined as elongation or contraction per unit length, whereas stress is defined as force per unit area. This modulus can be thought of as the resistance of a material to elastic deformation. The elastic modulus of a stiffer material is higher. The value of this modulus varies between 45 gigapascals for magnesium and 407 gigapascals for tungsten for most common metals.

Modulus of Elasticity

Elastic modulus is defined as the ratio of stress to strain below the proportional limit. It is a measurement of a material’s rigidity or stiffness. The modulus of elasticity is the slope of the stress-strain curve in the range of linear proportionality of stress to strain in terms of the stress-strain curve.

The higher the modulus, the stiffer the material is, and the lower the elastic strain caused by a given load. For calculating elastic deflections, the modulus is a crucial design parameter.

Young’s modulus is another name for elastic modulus, which is also known as modulus of elasticity.

Stress

The object deforms when the deforming force is given to it. An opposing force will be generated inside the item in order to restore the thing to its previous shape and size. This restoring force will have the same magnitude as the applied deforming force but will be in the opposite direction. Stress is the measurement of the restoring force created per unit area of the material.

As a result, stress is defined as the material’s restoring force per unit area.It’s a tensor quantity. The Greek letter is used to represent it. The unit of measurement of stress is N/m2. σ=FA is a mathematical expression.

Strain

The ratio of change in shape or size to the original shape or size is known as strain. Because it has no dimensions, it is stated as a number. Strain is a dimensionless term that defines the relative change in shape. Depending on the stress, the body can be subjected to two forms of strain.

The equation for strain is given as: ε=lL where, is the strain, l is the change in length and L is the original length.

Elastic constants

Elastic constants are the values that determine the amount of deformation caused by a certain stress system acting on a material.

Theoretically, elastic constants are utilised to determine engineering strain. The number of elastic constants in a homogeneous and isotropic material is four.

The types of elastic constants are:

  1. Young’s modulus, often known as the modulus of elasticity, is a measure of the elasticity of a material (E).
  2. Modulus of stiffness or shear modulus (G).
  3. Bulk modulus (K).
  4. Poisson Ratio ().

Unit of modulus of elasticity

Pascal is the unit of normal stress, but longitudinal strain has no unit. Because longitudinal strain is defined as the ratio of length change to original length. As a result, the unit of Modulus of Elasticity is the same as the unit of Stress, which is Pascal (Pa). The modulus of Elasticity is generally measured in Megapascals (MPa) and Gigapascals (GPa).

1MPa=106Pa
1GPa=109Pa

Facts related to Modulus of Elasticity

  • Young’s Modulus and Modulus of Elasticity are the same thing. The modulus of elasticity is a constant that varies from material to material.
  • It is introduced by Robert Hooke. The Early Scientist Who Worked on Applied Mechanics was Robert Hooke (1635–1703).
  • The value of E, according to Robert Hook, is dependent on both the geometry and the substance under discussion. Physical testing is essential for any new component in order to determine the value of E.
  • The value of E, according to Robert Hook, is dependent on both the geometry and the substance under discussion. Physical testing is essential for any new component in order to determine the value of E.
  • Elastic modulus is often referred to as tensile modulus or elastic modulus.
  • Every material has a fundamental property that cannot be altered. Temperature and pressure, on the other hand, play a role.
  • The Elastic Modulus is a measurement of a material’s stiffness. To put it another way, it’s a measurement of how easily a material can be bent or stretched.

It is the stress and strain diagram’s slope up to the proportionality limit.

Applications of Young’s Modulus

  • It’s employed in both engineering and medical science.
  • The elastic modulus can be used to determine how much a material will stretch as well as how much potential energy will be stored.
  • The elastic modulus can be used to predict how a material will react under stress.
  • Elastic modulus is also used to describe biological materials such as cartilage and bone.

Conclusion

We can assert that steel is more robust in nature than wood or polystyrene by studying its modulus of elasticity, since it has a lower tendency to deform under applied load. It is also used to calculate how amount of deformity of the material when it is subjected to a load.