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Show theoretically that the limiting value of Poisson's ratio are -1 and 0.5?
Wiki User
∙ 11y ago
If Y be Young's modulus, k be Bulk Modulus, n be Shear Modulus and s be Poisson's ratio, (poisson's ratio is ideally denoted by small sigma) then we have a few relations between them, two of which are:
- Y= 3k(1-2s) .....(1)
- Y= 2n(1+s) .....(2)
3k(1-2s) >= 0
so, (1-2s) >= 0
so, 2s=<1
so, s=< 0.5
From equation (2) we see that
2n(1+s) >= 0
so, (1+s) >= 0
so, s>= -1
so the value of s lies in between -1 and 0.5
>= denotes 'greater than or equal to' and <= denotes 'less than or equal to'
Hope this solves your problem.. :)
Wiki User
∙ 11y ago
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