# Poisson Ratio – its 3 [Formulas, Ratios Of Negative & Ratio in Common Materials]

## Poisson Ratio

The material will elongate on the axis of the load if the tensile load is applied to the material and if the load is compressive the axial dimension will decrease. In engineering analysis for determining the stress and deflection properties of materials, this ratio is required constant and it is also constant for structures like beams, rotating discs, plates, and shells.

For more than 200 years Poisson ratio has been a basic principle of engineering and allows engineers to identify how much a material can be compressed and stretched and before it collapses how much pressure it will withstand.

### Formula For Poisson Ratio:

μ = – εt / εl

where,

μ is the Poisson ratio

εt亚洲综合香蕉在线视频 is the transverse strain in m/m, ft/ft

εl is the longitudinal or axial strain in m/m, ft/ft As,

#### Longitudinal or axial strain can be expressed as;

εl = dl / L

εl is the longitudinal or axial strain in m/m, ft/ft or dimensionless

dl 亚洲综合香蕉在线视频is the change in length along the direction of force in m, ft

L 亚洲综合香蕉在线视频is the initial length along the direction of force in m, ft

#### Transverse or lateral strain can be expressed as;

εt = dr / r

εt 亚洲综合香蕉在线视频is the transverse or lateral strain in m/m, ft/ft or dimensionless

dr亚洲综合香蕉在线视频 is the change in radius in m, ft

r is the initial radius in m, ft

### Poisson Ratios For Common Materials;

 Materials Poisson’s Ratio – μ – Upper limit 0.5 Aluminum 0.334 Rubber 0.48 – 0.5 Indium 0.45 Gold 0.42 Lead 0.44 Copper 0.37 亚洲综合香蕉在线视频Polystyrene 0.34 Brass 0.33 Ice 0.33 Polystyrene foam 0.3 亚洲综合香蕉在线视频Stainless steel 0.30 Steel 0.29 Tungsten 0.28 Zinc 0.25 Boron 0.08 Beryllium 0.03 Re-entrant foam -0.7 Isotropic lower limit -1

### Negative Poisson Ratio Materials:

Some auxetic materials show a negative Poisson ratio and the transverse strain in the material will actually be positive when subjected to positive strain in a longitudinal axis and this is due to uniquely orient and hinged molecular bonds.

During a compression creep test certain wood display negative Poisson ratio and compression creep test shows positive Poisson ratios.

During constant loading Poisson ratio for wood is time-dependent and this means that strain in the axial and transverse direction don’t increase in the same rate and materials with a negative Poisson ratio have been called rubber, auxetic materials, and dilational materials. Some of auxetic materials are;

1. Tendons with a limited range of motions.
2. Polymers such as Gore-tex.
3. Polyurethane and graphene.

Negative Poisson ratio materials give the benefit of high energy absorption and possess high resistance and used for packing materials, medical knee pads and footwears, etc.

### Applications Of Poisson Effects:

Poisson effects have a considerable influence is in pressurized pipe flow and the air or liquid inside the pipe is highly pressurized and on the inside of pipe it exerts a uniform force and resulting in a hoop stress.

It might be helpful in improving the fracture of the composite and may be used in body armors.

### Points To Remember:

1. The lateral strain will be compressive if the longitudinal strain is tensile.
2. The longitudinal strain will be compressive if the lateral strain is tensile.
3. A longitudinal strain in the direction of the applied load is every time accompanied by an equal and opposite lateral strain.