How is the Poisson's Ratio Formula Derived?

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SUMMARY

The Poisson's Ratio formula, represented as dA = A(1 - m dL/L)^2 - A, calculates the percentage change in cross-sectional area (A) due to a percentage stretch in length (L). The variable 'm' denotes Poisson's ratio, which quantifies the relationship between longitudinal strain and lateral strain. The squared term in the formula accounts for the geometric relationship between area and length changes, reflecting the nonlinear nature of area variation under deformation. This derivation is crucial for understanding material behavior under stress.

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saravanan_n
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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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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
 
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
 
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