How is the Poisson's Ratio Formula Derived?

In summary, the equation dA=A(1-m dL/L)^2 -A is a formula for calculating the percentage change in cross-sectional area for a percentage stretch lengthwise, taking into account the compression of the width as the length is stretched. The squared term may be related to Poisson's ratio, which is a measure of the change in width relative to the change in length.
  • #1
saravanan_n
12
0
can anybody please tell me how this equation has been arrived?

dA=A(1-m dL/L)^2 -A


where
A=Area of cross section
L=length
 
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  • #2
saravanan_n said:
can anybody please tell me how this equation has been arrived?

dA=A(1-m dL/L)^2 -A


where
A=Area of cross section
L=length

Whithin what context did you acquire this equation ?

marlon
 
  • #3
What is m?

Looks to me it's a formula for calculating the % change in cross-sectional area for a % stretch lengthwise. Cross-section area is a function of the width (or perhaps width x length). But width is compressed as length is stretcehd and that has to be taken into account while calculating the change in area.

Having written all this, I don't get why a squared term is involved, because while the calculation of an area may involve a square, the change in such an area would be linear.

From a Yahoo search on "Poisson's ratio":
http://www.millersv.edu/~jdooley/macro/derive/elas1/poissn/poissn.htm
 
Last edited by a moderator:

What is Poisson's ratio?

Poisson's ratio is a measure of the ratio of lateral strain to axial strain for a given material. It describes how a material will change shape when subjected to a compressive or tensile force.

What is the significance of Poisson's ratio?

Poisson's ratio is significant because it can provide information about the stiffness, elasticity, and behavior of a material under stress. It is also used in engineering and material design to ensure the structural integrity and stability of structures.

How is Poisson's ratio calculated?

Poisson's ratio is calculated by dividing the lateral strain by the axial strain. It can also be calculated by measuring the change in diameter of a material when subjected to a compressive or tensile force.

What is a common value for Poisson's ratio?

The most common value for Poisson's ratio is between 0 and 0.5. Most materials have a Poisson's ratio within this range, with some exceptions such as rubber which can have a negative Poisson's ratio.

How does Poisson's ratio affect the behavior of materials?

Poisson's ratio affects the behavior of materials by influencing their stiffness, elasticity, and resistance to deformation under stress. Materials with a higher Poisson's ratio are more likely to deform in a specific direction when subjected to a force, while materials with a lower Poisson's ratio are less likely to deform and are considered more rigid.

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