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Poisson Ratio Calculator

This calculator presents three methods to determine the Poisson ratio of an object. Poisson ratio is the ratio of lateral strain and longitudinal (or axial) strain of a deformed object.


Calculators

Three methods to calculate Poisson ratio:

Method 1) Strains



Lateral strain, ε
:1​



Axial strain, ε
:3​



Poisson's ratio, ν
:0.33​


The equation is given by:

ν=ϵlateralϵaxial\nu = \dfrac{\epsilon_{lateral}}{\epsilon_{axial}}
Where:
  1. 
    
    is Poisson's Ratio (unitless)
  2. 
    
    is the lateral or transverse strain (m/m), which is the ratio between the change in width to the original width
  3. 
    
    is the axial or longitudinal strain (m/m), which is the ratio between the change in length to the original length


Method 2) Shear Modulus

❗This method is valid for isotropic materials only, which means the material has the same properties in all directions.


Shear modulus, G
:20GPa​



Young's modulus, E
:200GPa​



Poisson's ratio, ν
:Ratio needs to be between 0 and 0.5, Check the values and/or the signs​


The equation is given by:

G=E2(1+ν)→ν=E2G−1G = \dfrac{E}{2(1 + \nu)} \rightarrow \nu= \dfrac{E}{2G}-1
Where:
  1. 
    
    is the shear modulus, which is the ratio of the shear stress to the shear strain
  2. 
    
    is Young's Modulus (stiffness), which is the degree to which an object resists deforming in reaction to an applied force


Method 3) Length & Width Dimensions



Original length, l
:4mm​



Change in length, Δl
:1mm​



Original width, w
:2mm​



Change in width, Δw
:0.2mm​



Poisson's Ratio
:0.4​


The equation is given by:

ν=Δw/wΔl/l=ϵlateralϵaxial\nu = \dfrac{\Delta w/w}{\Delta l/l}=\dfrac{\epsilon_{lateral}}{\epsilon_{axial}}
Where:
  1. 
    
    is the original length, which is the length before deformation
  2. 
    
    is the original width, which is the width before deformation
  3. 
    
    is the change in length, which is the difference between the new length after deformation and the original length
  4. 
    
    is the change in width, which is the difference between the new width after deformation and the original width


Explanation

Poisson ratio is a measure of how a material deforms when it is stretched or compressed. It is the ratio of the change in width to the change in length of a material.
The ratio between the change in diameter, ΔD, and the original diameter, D is the lateral strain. The ratio between the change of the length, ΔL, and the original length, L, is the axial strain. The ratio between the lateral strain and the axial strain is the Possion ratio.
Object deforming due to being compressed longitudinally

For isotropic materials (materials with the same properties in all directions), the Poisson ratio could also be calculated using the Shear Modulus and Stiffness of the object using the following formulae:

.

Poisson ratio typically vary from 0 to 0.5.
  1. A Poisson ratio of 0.5 means the material expands laterally as much as it contracts longitudinally when under axial compression, and vice versa.
  2. A Poisson ratio of 0 indicates that the material experiences no lateral strain when under axial load, and vice versa.
  3. Auxetics are materials that have a negative Poisson ratio, which means they expand laterally when stretched longitudinally and vice versa.
Examples of Poisson ratio for common materials:
  1. Rubber, is an example of a material with a high Poisson ratio of around 0.5. When stretched, its length increases, but its width also decreases; when compressed, its length decreases, but its width increases.
  2. Cork, is an example of a material with a low Poisson ratio of almost 0. When stretched, its length increases, but its width does not decrease; when compressed, its length decreases, but its width does not increase.
  3. Concrete has a Poisson ratio of 0.2 as codified in AS 3600
  4. Structural steel has a Poisson ratio of 0.25 as codified in AS 4100


Related Resources

  1. 🔗 Relationship between Young's modulus, bulk modulus and Poisson’s ratio
  2. 🔗 Moment of Inertia Calculators
  1. 🔗 Shear Modulus Calculator
  2. 🔗 Elastic Section Modulus Calculator
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