What happens to Poisson’s ratio as a material approaches incompressibility?
- AIt approaches 0
- BIt approaches 0.5Correct
- CIt approaches 1
- DIt approaches infinity
Solution
Concept
Poisson's ratio of incompressible materials
Formula
NONE
Step-by-step solution
1. An incompressible material maintains constant total volume when subjected to mechanical strain. 2. The volumetric strain equation equals zero when Poisson's ratio equals 0.5. 3. Therefore, as a material approaches incompressibility, its Poisson's ratio approaches 0.5. Answer: B
Explanation
For isotropic elastic materials, volumetric strain under hydrostatic pressure is related to Poisson's ratio by a factor of (1 - 2v). When a material is incompressible, its volume does not change under stress, causing volumetric strain to equal zero. Setting this factor to zero yields a Poisson's ratio of 0.5, making option B the correct choice.
Why the other options are wrong
A) A Poisson's ratio of 0 means there is no lateral strain, not complete incompressibility. C) A value of 1 exceeds the upper limit of 0.5 for stable isotropic materials. D) Poisson's ratio is bounded between -1 and 0.5 and cannot reach infinity.
Shortcut
Incompressible materials have zero volumetric strain, giving a Poisson's ratio of exactly 0.5.
Common mistake
Selecting option C by assuming that total incompressibility corresponds to a Poisson's ratio of 1 rather than 0.5.
Correct answer: B) It approaches 0.5