94.
For a homogenous ,isotropic elastic medium, the
ratio{\frac{\lambda}{\mu}} of the Lame’s constants for Poisson
ratio(\nu)=0.3 will be
(Thanks to Saroja)
solution:
{\frac{\lambda}{\mu}}
= ?
Poisson
ratio (\upsilon) = 0.3
Formulas:
\lambda = \frac{\nu E}{(1+\nu)(1-2\nu)}
\mu = \frac{E}{2(1+\nu)}
\frac{\lambda}{\mu}=\frac{\frac{\nu
E}{(1+\nu)(1-2\nu)}}{\frac{E}{2(1+\nu)}}
=\frac{2\nu}{(1-2\nu)}
=\frac{2*0.3}{(1-(2*0.3))}
=\frac{0.6}{1-0.6}
=\frac{0.6}{0.4}
\frac{\lambda}{\mu}=
1.5
Reference : Fundamentals of Geophysics by William Lowrie.
This question is also solve in this method
ReplyDelete(σ) =λ\2(μ +λ )
0.3= λ\2(μ +λ )
0.6(μ +λ ) =λ
0.6μ = λ-0.6λ
0.6/0.4 =λ /μ
1.5 =λ /μ
Yes, Nice solution. Thank you
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