Relations among Elastic Moduli
In homogeneous isotropic linear elasticity, Young's modulus Y, bulk modulus K, shear modulus G, and Poisson's ratio nu obey fixed algebraic relations; these relations do not apply unchanged to anisotropic media.
Why this shows up in the exam
Converting tabulated material constants · Checking plausible modulus values · Solving mixed deformation questions
Learn the idea
For an isotropic linear solid, any two independent elastic constants determine the others. Stretching, squeezing, and shearing describe different deformation modes, but isotropy ties their resistance together through Poisson's ratio.
🧠 Memory hook: Two isotropic elastic constants determine the family.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Y = 2G(1+nu) — Young-shear-Poisson relation
- Y = 3K(1-2nu) — Young-bulk-Poisson relation
- Y = 9KG/(3K+G) — relation eliminating Poisson's ratio
How to approach it
- 1Identify the two known independent constants
- 2Choose the relation with the fewest unknowns
- 3Check positivity and the physically allowed Poisson range
Common slip-ups that cost marks
- •Using rigidity modulus as Young's modulus
- •Applying isotropic relations to anisotropic materials
- •Mixing symbols for Poisson's ratio and shear modulus
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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