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Poisson's Ratio: Formula, isotropic elastic, anisotropic, viscoelastic materials, Properties, Effects of Temperature and Applications

Poisson's ratio is an essential part of the elasticity of materials. It is a scalar quantity and has no units since it is a ratio.

The precise definition states that the negative ratio of the transverse strain to the axial or longitudinal strain is called Poisson's ratio. It is the measurement of the expansion or the contraction experienced by a material in a direction perpendicular to the direction the force is applied.

It is also said to be the ratio of the transversal elongation to the axial compression experienced by a material. Mostly, the value of this ratio for any material ranges from 0.0 to 0.5. Here, the compressive deformation is considered to be negative and the tensile deformation to be positive

Poisson’s ratio of an isotropic elastic material-

The range of 0.0 to 0.5 mentioned above is due to the stability provided by this isotropic nature, and the material's elasticity should be positive. The ideal condition is considered on a usual basis in the material being a linear isotropic elastic homogeneous solid.

Poisson’s ratio for anisotropic materials-

Materials such as honeycombs, single crystal and other fibrous compounds are considered to be anisotropic. The direction in which they are stretched, or bent determines the physical properties such as elastic moduli and Poisson's ratio of these anisotropic materials. The value of their Poisson's ratio can either be positive or negative, depending on the direction.

Poisson’s ratio for viscoelastic materials-

When it comes to such materials, the Poisson’s ratio also depends on the frequency and the phase angle if the expansion or contraction of such a material is demonstrated in a sinusoidal nature.

Some basic properties of Poisson’s ratio are given below:

  • This ratio is different for every material as it depends on how each material reacts to the strain applied to it. The value of this ratio is a constant value for any material as long as it lies within the elastic limits.
  • The value of this ratio is not universal or the same for every material. Different configurations of every material have a different Poisson ratio.
  • The elongation or compression of material is done in the same horizontal plane as the force is applied. This means that if a force is applied to the width, there will be a change in the material's width. The negative sign of the ratio indicates if there will be an increase or a decrease in the elongation of the material when a force is applied to it.
  • Poisson's ratio is directly proportional to the extent of deformation of a body. The lesser the Poisson's ratio, the more deformation of a body will also be less.

Effect of temperature on Poisson’s ratio of materials:

It is observed that Poisson’s ratio of materials may be affected slightly by the temperature. Even though the lateral and longitudinal strains change their shape simultaneously in hot or cold conditions, there is a slight decrease in the ratio with the increase in temperature.

Effect of phase transformation on Poisson’s ratio of materials:

Even though the bulk modulus softens near a phase transformation, the shear modulus is not affected by it. However, the Poisson's ratio decreases near the surroundings where the phase transformation occurs and can also decrease to negative values.

Applications of Poisson’s ratio:

  • Fluid pipelines -
    Such fluid pipelines have a very high pressure acting on the interiors of the wall due to the continuous flow of water in these pipes. The strong flowing water exerts a constant force on these walls, which might result in the deformation of the walls. This increases the risk of leakage and discontinuity of the passage of water. This can be prevented by ensuring the materials which are used have a high Poisson's ratio.
    Material strength -
    It is important to know the intensity of the Poisson's ratio of material before creating an alloy. You should know what sort of materials you would want to use for alloys, depending on their ratios. Places with a high strain environment do not need materials with a high Poisson's ratio as they are more prone to deformation.
  • Cork used as bottle stopper -
    The main job of a cork is to act as a stopper and remain unchanged when an external force is applied to it. This is done by choosing high Poisson’s ratio materials instead of lesser ratio ones such as rubber.

Poisson's ratio is a great concept that works well in many applications in our daily lives. It is an essential property of a material.




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