Question
The relation between $\gamma ,\,\eta $ and $K$ for a elastic material is
✓
Answer
$\mu=$ Modulus of Rigiditg
$k =$ Bulk Modulus.
$\sigma=$ Normal stress
$y =3 k (1-2 \sigma)-(1)$
$y =2 \eta(1+\alpha)-(2)$
$\frac{ y }{3 k }=1-2 \sigma-(3), \frac{ x }{2 \mu}=1+\sigma-(4)$
Multiply eq $4$ by $2$.
$\frac{ y }{3 k }+\frac{ y }{\mu}=3-(5)$
Adding equ" $(3)$ and eqn $(5)$
$\frac{ y }{3 k }+\frac{ y }{\mu}=3$
$\frac{1}{3 k }+\frac{1}{\mu}=\frac{3}{ y }$
$\frac{1}{ y }=\frac{1}{9 k }+\frac{1}{3 \mu}$
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