Poisson's Ratio
The ratio of lateral strain to longitudinal strain when a material is stretched or compressed.
What is Poisson's Ratio?
The ratio of the magnitude of lateral strain to the magnitude of longitudinal strain in a material under stress, with a negative sign included to make the ratio positive for most materials.
Key formula / rule: Poisson's Ratio
Key points
- Define Poisson's ratio.
- Calculate Poisson's ratio given lateral and longitudinal strains.
- Understand the physical significance of Poisson's ratio.
- Relate Poisson's ratio to volume changes during elastic deformation.
Common exam trap
Forgetting the negative sign in the definition, leading to incorrect calculations.
Definitions
- Term
Poisson's Ratio (ν)
- Meaning
The ratio of the magnitude of lateral strain to the magnitude of longitudinal strain in a material under stress, with a negative sign included to make the ratio positive for most materials.
- Term
Lateral Strain
- Meaning
The strain perpendicular to the direction of applied force. For a wire under tension, it is the ratio of the change in diameter to the original diameter.
- Term
Longitudinal Strain
- Meaning
The strain in the direction of the applied force. For a wire under tension, it is the ratio of the change in length to the original length.
Learning objectives
Define Poisson's ratio.
Calculate Poisson's ratio given lateral and longitudinal strains.
Understand the physical significance of Poisson's ratio.
Relate Poisson's ratio to volume changes during elastic deformation.
Formulae
- Name
Poisson's Ratio
- Note
Where \εlateral is the lateral strain (e.g., change in diameter / original diameter) and \εlongitudinal is the longitudinal strain (e.g., change in length / original length). The negative sign ensures that \ν is positive for most materials, as lateral strain is usually opposite in sign to longitudinal strain.
- Expression
\ν = -\frac{\εlateral}{\εlongitudinal}
- Name
Volume Change Relation (Approximate)
- Note
This formula is valid for small strains and shows how volume change depends on longitudinal strain and Poisson's ratio. If \ν = 0.5, \Δ V/V = 0, meaning no volume change.
- Expression
\frac{\Δ V}{V} \≈ \εlongitudinal (1 - 2\ν)
Prerequisites
Stress and Strain
Young's Modulus
Elastic Limit
Common mistakes
Forgetting the negative sign in the definition, leading to incorrect calculations.
Confusing lateral strain with longitudinal strain.
Assuming Poisson's ratio is always 0.5.
Not understanding that it's a ratio of strains, not stresses.
Keywords
Poisson's Ratio
Lateral Strain
Longitudinal Strain
Elasticity
Material Properties
Strain
Stress
Volume Change
Practice preview
For an elastic material, Poisson's ratio is typically in the range:…
easy
If a wire is stretched, its length increases. What happens to its lateral dimension (e.g., diameter)?…
easy
A wire of length 1 m and diameter 2 mm is stretched by a force. Its length increases by 0.2 mm and its diameter decreases by 0.0001 mm. Calculate Poisson's ratio for the material of the wire.…
medium