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CSIR-NET JUNE 2019

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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.

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  1. Sunny jha (Patna)12 January 2022 at 19:14

    This question is also solve in this method

    (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

    ReplyDelete

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