# POISSON’S RATIO

## Define poissons ratio-

Poisson's ratio is the ratio of transversal expansion to axial compression, and it is symbolized by the Greek letter 'nu.' It is named after Simeon Poisson. The strain symbol is given by ε.

What is poisson ratio? Or how poisson’s ratio work? Or poisson’s ratio definition :-

“The ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force,” as described by Poisson. Here,

• Compressive deformation is regarded as negative.

• Tensile deformation is regarded as a positive.

 Symbol Greek letter ’nu’,v Formula Poisson’s ratio= -lateral strain/Longitudinal strain Range -0.1 to +0.5 Unit Unitless Scalar/vector Scalar quantity

Poisson’s formula

In the middle, it will compress. If the rubber's original length and width are L and B, respectively, it will tend to compress laterally when tugged longitudinally. To put it another way, the length has increased by dL and the breadth has increased by dB.

In this instance,

The Poisson ratio formula is as follows:

εt= −dB/Bεl= −dL/L

where is εt Transverse Strain.

εl Longitudinal Strain

Poisson's ratio=Transverse Strain/Longitudinal Strain

The Lateral or Transverse Strain is εt what it's called.

The Longitudinal or Axial Strain is denoted by the letter εl.

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The Poisson's Ratio -

The change in dimension (length, breadth, area, etc.) divided by the original dimension is the strain.

Strain-

The term "strain" refers to how much an object has been stretched or deformed. When force is applied to an item, strain occurs. Strain is primarily concerned with the object's length change.

Lateral or transverse strain-

The ratio of the change in diameter of a circular bar of a material owing to longitudinal deformation to its diameter is defined as lateral strain, also known as transverse strain. Because it is a ratio between two quantities of the same dimension, it is a dimensionless quantity. Lateral strain formula is given by multiplication of Poisson ratio and longitudinal strain.

Longitudinal or axial strain-

A material elongates in the axial direction while contracting in the transverse direction when subjected to a tensile force P. Transverse strain is contraction in the transverse direction, while longitudinal strain is elongation in the axial direction.

Poisson’s effect-

When a material is stretched in one direction, it compresses in the opposite direction, and vice versa. The Poisson's ratio is used to calculate the magnitude of this occurrence. When a rubber band is stretched, for example, it tends to get thinner.

Poisson’s ratio value for different material-

It is the ratio of transverse contraction strain to longitudinal extension strain, in the direction of the stretching force. For tensile deformation, Poisson's ratio is positive. For compressive deformation, it is negative

• Poisson's ratio is positive for tensile deformation.

• It is negative for compressive deformation.

Despite the fact that the longitudinal strain is positive, the negative Poisson ratio indicates that the material will experience a positive transverse strain.

Range of poisson’s ratio-

For most materials, the Poisson's ratio is between 0 and 0.5.

For various materials, a few examples of Poisson ratio are presented below-

 Material Values steel 0.27- 0.30 rubber 0.4999 concrete 0.1-0.2 clay 0.30-0.45 gold 0.42-0.44 cork 0.0 glass 0.18-0.3 copper 0.33 foam 0.10-0.50 stainless steel 0.30-0.31 cast iron 0.21-0.26

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