Answer to Question #170883 in Mechanical Engineering for bin

Question

Find a household material wherein you can demonstrate Poisson's Ratio and provide a short video clip wherein the change in longitudinal and lateral dimensions can be shown.

Answer 1

Consider an eraser made of rubber. Now first of all let's define Poisson's ratio.

When a piece of rubber in its original shape that is cuboid is pulled along its sides what happens? The rubber will get compressed from the middle. The original length and breadth of the rubber, which is L and B respectively when pulled longitudinally it, gets compressed laterally. The length of the rubber increase by the amount of dL and the breadth increases by dB.

εt= -dB/B

εl= dL/L

The formula for Poisson's ratio is, $\mu$ = —εt/εI

εt is the Lateral or Transverse Strain.

εl is the Longitudinal or Axial Strain, $\mu$ is the Poisson's Ratio

The ratio of the transverse contraction of a material to the longitudinal extension strain in the direction of the stretching force is the Poisson's Ration for a material. The stress or stain can be generated by applying the force on the material by the body. The Poisson's ratio is negative for the compressive deformation whereas for the tensile deformation the Poisson's Ratio is Positive. The negative Poisson's ratio suggests that the positive strain is in the transverse direction. The Poisson's Ratio for most of the materials is in the range of 0 to 0.5.

The Poisson's Ratio is between the range f 0 to 0.5 for plastics. When the Poisson's Ratio is 0 there is no reduction in the diameter or one can even say there is no laterally contraction happening when you are elongating the material but the density would reduce. The value of 0.5 indicates that the volume of the material or object will remain the same or constant during the elongation process or when the diameter decreases of material when the material is elastomeric.

Following is the different Poisson's Ratio for different materials.

Rubber = 0.49

Aluminium = 0.32

Concrete = 0.2

Cork = 0

Usually, Poisson's Ratio is positive because most of the common materials when stretched becomes narrower in the opposite or cross direction. Most of the materials resist the change in volume which is determined by the bulk modulus K or also called B more than they resist change in shape which is determined by the shear modulus G. The interatomic bonds also realign with the shape deformation.