Chapter 15, Problem 15D.1P

Interpretation Introduction

Interpretation:

Lame constants have to be used to confirm the relations between Young’s, bulk and shear modulus.

Concept Introduction:

Young’s modulus: $E=\frac{uniaxialstress}{uniaxialsrain}$

Bulk modulus: $K=\frac{pressure}{fractionalchangeinvolume}$

Shear modulus: $G=\frac{shearstress}{shearstrain}$

The three moduli can be related as follows,

  $\begin{array}{l}G=\frac{E}{2\left(1+V_p\right)}\\ \\ K=\frac{E}{3\left(1-2V_p\right)}\end{array}$