Elasticity

Longitudinal strain, εL=0.2%=0.002
Poisson's ratio, µ=0.3
We are asked to find the volume strain (εV).
Step 1: Recall the formula for volume strain
For small deformations,
Volume strain =εV=εL(1−2µ)
However, to be more precise, the change in volume ∆V∕V=εL+2εt,
where εt=−µεL (lateral strain is negative if the material stretches longitudinally).
So,
‌‌

∆V

V

=εL+2(−µεL)
‌⇒εV=εL(1−2µ)
Step 2: Substitute the values
‌εV=0.002(1−2×0.3)
‌εV=0.002(1−0.6)
‌εV=0.002×0.4=0.0008
Step 3: Convert to percentage
εV=0.0008×100=0.08%
Final Answer:
0.08%