?For an isotropic substance, the moduli and Poisson’s ratio may be expressed in terms of

Chapter 15, Problem P15D.1

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For an isotropic substance, the moduli and Poisson’s ratio may be expressed in terms of two parameters λ and μ called the Lamé constants:

\(E=\frac{\mu(3 \lambda+2 \mu)}{\lambda+\mu \quad K=\frac{3 \lambda+2 \mu}{3} \quad G=\mu\) \quad v_{\mathrm{P}}=\frac{\lambda}{2(\lambda+\mu)}\)

Use the Lamé constants to confirm the relations between G, K, and E given in eqn 15D.3.

Text Transcription:

E=mu(3 lambda+2 mu)/lambda+mu

K=3 lambda+2 mu/3

G=mu

v_P=lambda/2(lambda+mu)